Most glitches occur randomly, and none of them seem to be platform specific so far (unless there is something wrong with XBOX autosaves).
Use the following thread to report your bugs. List compiled and maintained by Cog from Tomb Raider Forums.

General
G1.([s]PC-Yes[/s];PS3-?;360-?)
Bug: Loading a saved game in treasure hunt causes the game to think you're playing story mode - 'Field Assistance' is enabled, 'Revisit Location', on the other hand, is not.
Solution: Kill Lara.
UP: should be fixed in v1.1 (PC)
G2. (PC-Yes;PS3-Yes;360-Yes)
Bug: Lara gets stuck in an animation loop (is 'stuck in a texture' in some cases).
Solution: Release any directional keys, bringing Lara to a 'full stop', then move/jump away from the glitchy spot. Alternatively, shoot your guns. Some seriously freaky loops may require a restart.
G3. (PC-Yes;PS3-?;360-?)
Bug: During the Headshot move, instead of reticule, the player suddenly takes control of the camera.
Solution: N/A. Seems to randomly go away after reloading the level/checkpoint.
G4. (PC-Yes;PS3-Yes;360-Yes)
Bug: Flashlight disappears - 'On/Off' key has no effect and the PLS itself is no longer listed in your inventory. Has something to do with Treasure hunt and Lara's bike most of the time (could be that its light interferes with Lara's flahslight, as the PLS automatically turns off when you get on the bike), but there are reports of this happening in other levels (namely, Manor).
Solution: N/A. Restart the level.
G4a. (PC-?;PS3-?;360-?)
Mostly a problem in Mexico, but may happen in other levels too.
Bug: Quest items disappear from the inventory, meaning you can't use them.
Solution: N/A. Reload.
G5. (PC-Yes;PS3-Yes;360-Yes)
Bug: Unresponsive controls due to animation quirks. For example, if you nearly push Lara off the edge and she does her 'flail' motion, you may not be able to move into the direction you want afterwards. Or: while standing on a beam/pole she refuses to walk.
Solution: Generally, moving/jumping/turning in different directions solves this. On poles, you can also drop down ('crouch' key) and climb it once again.
G5a. (PC-Yes;PS3-Yes;360-?)
Bug: Lara won't make the 90º degree turn in 'inside corner ledges' if you drop to the ledge near the corner
Solution: Move Lara in the oposite direction, and then again in direction of the corner you want to turn.
G5b/G6a. (PC-Yes;PS3-Yes;360-Yes)
Bug: Attempts to pick up an object (usually a medkit) causes an 'animation loop', where Lara awkwardly circles around the object until she picks it up. The loop may also continue even without the eventual pick up, in which case Lara may fall through the ground. (A more disturbing example of this bug.)
Solution: See G6.
G6. (PC-Yes;PS3-?;360-Yes)
Bug: Lara has trouble detecting objects she can interact with, and the 'Interact' key causes melee attack in most cases.
Solutiuon: Make sure Lara is close to the object, is facing it and, preferably, stands still.
G7. (PC-Yes;PS3-?;360-?)
Bug: Something causes Lara to get stuck in some kind of ragdoll state, yet she is 'alive' and can fire her guns, open the PDA etc.
Solution: N/A. Reloading your last checkpoint fixes it, most likely.
G8. (PC-Yes;PS3-Yes;360-Yes)
Bug: Lara dies upon bumping into some specific object in the level (for example, wooden ramps in Xibalba corridor or ACME Smash Blocks in one of the Xibalba trial rooms).
Solution: Well...avoid bumping into such objects (note: this bug is particularly random).
G9. (PC-Yes;PS3-Yes;360-Yes)
Bug: Lara falls through the ground/seabed or, occasionally, even through walls (during walljumps). The latter may be location specific.
Solution: N/A. Restart the level/last checkpoint.
G10. (PC-Yes;PS3-?;360-?)
Bug: When a savegame is loaded Lara appears at an older checkpoint. Nothing else is affected (id est in Mexico bike appears where it should - at the real last checkpoint). Sometimes it's the other way around - Lara spawns where the last checkpoint was, yet other objects (like movable blocks) are reset to their previous/default positions.
Solution: N/A.
G10a. (PC-?;PS3-?;360-Yes)
Bug: A weirder version of the above - loaded checkpoint not only precedes the one actually saved, but is also on a previous level. The previous level itself is glitched and cannot be completed. Reports state it also corrupts savegames.
Solution: N/A.
G11. (PC-?;PS3-?;360-?)
Possibly location specific.
Bug: Occasionally some cutscenes may not start at all (like the one triggering transition from Med.Sea ruins to the ship), and thus the level cannot be finished.
Solution: N/A. Restart the level/checkpoint (latter may not help).
G12. (PC-Yes;PS3-?;360-?)
Bug: Poles you pick up from the ground may disappear once you drop them.
Solution: If it disappears, reload. Otherwise avoid dropping them in the open.
G12a. (PC-Yes;PS3-?;360-?)
Bug: Poles you drop are still there where you left them, but cannot be picked up again.
Solution: N/A. Reload.
G13. (PC-Yes;PS3-?;360-Yes)
Bug: Lara becomes invisible for no apparent reason.
Solution: Kill Lara/Reload your last checkpoint/Restart.
G14. (PC-?;PS3-Yes;360-?)
Possibly location specific (reported @ Arctic, bossbattle).
Bug: The screen goes blank, yet the game is running. If there was an autosave during that time, loading it won't fix the problem.
Solution: N/A. Restart the level or load a normal manual save.
G15. (PC-Yes;PS3-Yes;360-?)
Bug: Quick shimmy round the corner causes animation glitches.
Solution: Go back to normal speed before hitting the corner.
G16. (PC-Yes;PS3-?;360-?)
Bug: Attempting to save the game manually results in Crash-to-Desktop.
Solution: N/A. Probably hardware/OS-related.
G17. (PC-Yes;PS3-?;360-?)
Bug: Due to the fact that most, if not all, important physics based events are non-scripted real-time events, random collison glitches may severely hinder or even prohibit the game progress.
Solution: See specific cases of this bug (S14, for example).
G18. (PC-Yes;PS3-Yes;360-?)
Bug: Manual Treasure Hunt savegames are overwritten/deleted for no apparent reason. Seems to be caused by saving at one level, and then loading some other save from the level before it.
Solution: N/A.
G19. (PC-Yes;PS3-Yes;360-?)
Bug: Because of real-time nature of all the in-game cutscenes, skipping them may lead to various oddities.
Solution: Don't skip the cutsenes. Or don't do it too fast, at least.
G20. (PC-?;PS3-Yes;360-?)
Bug: Gauntlet/belt magicks disappear for reasons unknown (possibly a 'no-flashlight' type glitch?).
Solution: Reload an earlier checkpoint.
Location specific
S1. (PC-?;PS3-?;360-?)
Location: Thailand (Treasure Hunt)
Bug: When replaying the level and entering Thor's Hall from the pit room, the bridge is facing the exit and there's no way to bring it back.
Solution: N/A. Restart the level (you may have to do this more than once). By default, the bridge should automatically return to its original position when you get close. Alternatively, use a trainer to bypass the gap (PC only).
S1a. (PC-Yes;PS3-?;360-?)
Location: Thailand (Treasure Hunt)
Bug: While the bridge resets its position when you re-enter the hall, attepts to move it cause the whole structure to swing around violently to the statue, where the relic is/was. It is then stuck in that position and cannot be moved.
Solution: Unless you have made a savegame before trying to move the bridge, it seems like a permanent glitch.
S1b. (PC-?;PS3-Yes;360-?)
Location: Thailand
Bug: Dying after acquiring the gauntlet may cause Thor's power to vanish.
Solution:N/A. Reload.
S2. ([s]PC-Yes[/s];PS3-?;360-Yes)
Location: Mexico
Bug: In the Xibalba corridor, first wooden ramp/bridge is lowered.
Solution: N/A. Restart the level (you may have to do this more than once). Alternatively, use a trainer to bypass the gap (PC only). Eidos' take on the problem
UP: should be fixed in v1.1 (PC)
S3. (PC-Yes;PS3-?;360-?)
Location: Mexico
Bug: In Thor's chamber, hanging on lower snake's pole does not close its mouth and therefore its eitr flow won't stop.
Solution: N/A. Try restarting from the last checkpoint or reloading the level itself (unconfirmed).
S4. (PC-Yes;PS3-?;360-?)
Incarnation of G10 most likely.
Location: Bike levels (usually in Treasure Hunt)
Bug: The bike disappears after loading a savegame.
Solution: Kill Lara. If it does not help, restart the level.
S5. (PC-Yes;PS3-Yes;360-Yes)
Location: Mexico
Bug: No rain in the very beginning of the level (isn't limited to this area though). Usually happens in Treasure Hunt.
Solution: Drive to the next section of the map (via the underground tunnel). Rain will reappear in all parts of the map.
S6. (PC-?;PS3-?;360-?)
Location: Thailand (though looks like it's of a general kind).
Bug: Violating the programmed gameflow (for example, bypassing some important object; in this case - the 'falling platform' sequence) causes extreme graphical glitches.
Solution: Since it's an abnormal bug (as attempts to skip game triggers usually end in Lara's death, otherwise it's an exploit), only option is to restart the level.
S7. (PC-?;PS3-Yes;360-?)
Location: Mexico
Bug: After failing to enter Xibalba for the first time, calendar plates get stuck and none of them can be operated.
Solution: N/A. Restarting the level may help. As a precaution, don't save the game right after solving the second calendar puzzle and before the motorcycle run to the exit.
S7b. (PC-Yes;PS3-Yes;360-?)
Location: Mexico
Bug: Another Xibalba entrance problem - when trying to exit, Lara may refuse to place the missing jaguar head, but will pull the switch afterwards - doors won't open, but the lever will become inoperable.
Solution: N/A. Restart/Reload.
S8. (PC-Yes;PS3-?;360-Yes)
Location: Mediterranean Sea
Bug: If you pull the lever too soon after dropping the right-hand statue's head for a weight, the door to Niflheim may not open, although the cutscene plays.
Soluion: N/A. Since the cutscene triggers a checkpoint, there's no other way than to a load a previous save or restart the level.
UP: Seems like it's fixed in v1.1 (PC), or, at least, that's what 'fixed issue with door lever at Kraken room entrance' implies.
S9. (PC-?;PS3-?;360-?)
This one may be a variation of G6.
Location: Thailand
Bug: Occasionally, after collecting the two gemstones for Shiva's arm puzzle, no icon apears for you to insert them (id est Lara refuses to insert them).
Solution: N/A. Reload a save where you are yet to collect the stones.
S10. (PC-Yes;PS3-?;360-?)
An incarnation of the G11 glitch.
Location: Arctic
Bug: Amelia cutscene doesn't play - the player can explore the area with Amelia just standing there.
Solution: N/A. Restart/Reload.
S11. (PC-?;PS3-Yes;360-?)
Location: Thailand
Bug: If Lara is bitten by a spider while grappling the wall ring above the pool after the Thor's hall, she may fall into the water with her body 'frozen' - one arm held up awkwardly at an angle. She won't dive or move to get out of the water, but still can move across the surface.
Solution: N/A. Reload.
S12. (PC-?;PS3-?;360-?)
Location: Croft Manor
Bug: Activating the lever to end the crypt part of the level and then sprinting into the corridor may bypass the section loading trigger, resulting in no actual level and, as a result, nothing for Lara to stand on. Does not happen if Lara walks/runs into the corridor. (May have something to do with hardware-related with loading times, but who knows.)
Solution: N/A. Reload.
S13. (PC-?;PS3-Yes;360-?)
Location: Croft Manor
Bug: Using grenades against tiger thralls freezes the system. May be related to nagas' 'no-grenade-death-animation' oddity.
Solution: Reload. Don't use grenades.
S14. (PC-Yes;PS3-?;360-?)
Location: Croft Manor
Bug: If a part of the now dead tiger thrall ends up in the way of the column the player has to push, a collision glitch may cause the column to jump and land in a position when one can no longer move it.
Solution: Try to blast the piece of junk away with your grenades or simply reload.
S14a. (PC-Yes;PS3-?;360-?)
Location: Croft Manor (Prologue)
Bug: Grappling the door and then pulling it sometimes produces a collision glitch when doors ends up blocking the way.
Solution: N/A. Reload.
S15. (PC-Yes;PS3-?;360-?)
Perhaps intended.
Location: South Mexico.
Bug: In Thor's chamber failing to navigate the set of crumbling ledges (either due to 'wrong-checkpoit-reload' bug, Lara's refusal to navigate the ledges, or simply escaping the situation and returning to the highest level) may close the only obvious way down.
Solution: Reload an earlier save or try searching hte threads for a 'glitched' way down.
S16. (PC-Yes;PS3-?;360-?)
Location: Croft Manor
Bug: Skipping the gauntlet/thralls cutscene too fast will cause the thralls to activate incorrectly, and they will not come after Lara.
Solution: Commit suicide to reset the thralls, or simply ignore the glitch.
S17. (PC-Yes;PS3-Yes;360-?)
Example of G19.
Location: Croft Manor
Bug: Dying after killing the thralls but before reaching the next checkpoint will cause the game to load with the thralls alive, but the ammo and grenades you may have used for killing them previously will be gone.
Solution: Try not to die.
S18. (PC-Yes;PS3-?;360-?)
Another G10.
Location: Mexico
Bug: Flooding the room on your way up and killing Lara in the process messes up the savestate - upon loading Lara spawns at the checkpoint, yet the room is already filled with eitr, and this leads to instant death.
Solution: Reload an older manual save.
S18. (PC-Yes;PS3-Yes;360-?)
G17 collision glitch?
Location: Mexico
Bug: The runic column you have to push after acquiring Thor's hammer possess a will of its own, apparently - reports note its habit to return to its original position ore even fly away when attempting to move it.
Solution: Restarting/loading may help. See if there are any thrall remains in column's way - those may cause the glitch.
S19. (PC-?;PS3-Yes;360-?)
Likely to happen in other bike levels.
Location: Mexico
Bug: The Bike is stuck at the point where, on tiyr way back, you have to move the small obstacle after acquiring the belt.
Solution: Place the bike more carefully? Seems like another collision problem.
S20. (PC-Yes;PS3-Yes;360-?)
Location: Med Sea
Bug: Lara cannot dive and stays underwater on the same height as her yacht.
Solution: N/A. Restart the level
Oddities
- (PC-Yes;PS3-?;360-?) models of Thor's gauntlets and belt are floating underwater near the starting point in Arctic (seems to be fixed in v1.1);
- (PC-Yes;PS3-Yes;360-?) camera goes nuts when attempting to drop down safely (using the 'crouch' key) and grab a corner ledge;
- (PC-Yes;PS3-Yes;360-?) camera goes nuts when attempting to exit a crawlspace that ends with a ledge (in fact, any crawlspace will do);
- (PC-Yes;PS3-?;360-?) when a grenade kills naga, the latter has no ragdoll-animated death - its carcass simply floats in the air;
- (PC-Yes;PS3-?;360-?) attempts to bypass the underwater boundaries in the Arctic level seem to cause the game to eliminate the underwater environment altogether;
- (PC-Yes;PS3-?;360-?) above also applies to Mediterranean, the 'God of Thunder' chapter (note, this glitch is reported to freeze the Xbox version);
- (PC-Yes;PS3-Yes;360-?) some enemies can enter the state of 'utter stupidity' - they run in circles, ignoring Lara (and some cannot be killed);
- (PC-Yes;PS3-?;360-?) after dying, Lara is spawned with the grenade model stuck up her left gun holster (press 'throw grenade' + 'roll' to get rid of it);
- (PC-Yes;PS3-Yes;360-?) certain jumps towards ledges (especially corners) temporarily embeed Lara into the texture;
- (PC-Yes;PS3-?;360-?) falling into eitr in Arctic allows you to see the out-of-boundaries area;
- (PC-?;PS3-?;360-Yes) starting a new game while playing Prologue (or something else) may produce static shadows/lightning instead of dynamic;
- (PC-Yes;PS3-?;360-?) it is possible to bypass the trigger for the Puppet No Longer chapter in Thailand by not moving the bridge to its defined position - you can still finish the level though;
- (PC-Yes;PS3-?;360-?) upon death corpses of those slain by Lara demonstrate various unusual behaviours, like getting stuck halfway through the floor or bouncing up and down;
- (PC) 1280*1024 (5:4) resolution stretches the picture;
- (PC-Yes;PS3-?;360-?) Lara's 'physics-powered' strands of hair go f.u.b.a.r. in some situations (when stanfing on a pole, for example);
- (PC-Yes;PS3-Yes;360-?) Lara's hand is painfully bent during the cinematics;
- (PC-Yes;PS3-?;360-?) skipping early the first Med Sea cutscene causes the 'one weel earlier' line to stay on-screen indefinitely (kill Lara to fix this) (this is a G19 glitch);
- (PC) Anisotropic Filtering doesn't work (maybe hardware-related, as i've seen reports of everything working as it should - can't spot the difference myself);
- Bathing Suit has heavy boot footstep sounds.
- (PC-?;PS3-Yes;360-?) at one point in the last portion of the game you can witness [url=http://www.youtube.com/watch?v=IumlDd3HFvw]Natla freezing in mid air[/b] - she stays that way until you trigger her next move.
- (PC-?;PS3-Yes;360-?) shoot the assault rifle until the magazine is empty, then stop aiming - reload animation is cancelled, but a floating magazine will insert itself into the rifle anyway.
- (PC-Yes;PS3-likely;360-likely) schools of fish may bump innto the rock and stay there, swim around them to 'frighten their AI';
- (PC-Yes;PS3-likely;360-likely) Lara has funky collisions with sloped or otherwise uneven surfaces, can be observered while standing on the yacht - Lara floats when yacht comes down and bends her legs when it goes up with the waves;
Platform specific
X360
Bug: The 'Master Speed Demon/Master Swan Dive' achievement may not register even though all requirements have been met
Solution: Word is, you have to get them in one adventure, otherwise the big achievement won't register (ie don't leave them for Treasure Hunt).
[b]Also[/n]: If you plan to take a break and not do these all in one go, make sure that you get a checkpoint after completing each of these achievement tasks or else it won't unlock. So you can't just save, exit gameplay, and load the game later on. But you may get the checkpoint first, then save and load. Of course, you need to have passed them successful otherwise you need to reload a save file right before the failed task. These achievements are glued to your save file and autosave - load those only and not the ones for any other different 'New Game' adventure (Ring_of_Fire).
Wii
Location: Thailand Level
Bug: After completing the gauntlet chamber, a lever is missing which is required to open the exit.
Solution: Restart the game and do not save before getting past that room. This bug has been resolved.