There was a bug for me on 360 involving an elevator in the sewer area in which Batman would fall through the floor as the elevator was going up, leading to him landing in the water, climbing out onto nothing, then going into a permanent free-fall beneath the map.
And another bug involving that same elevator occurred towards the end of the game when I was backtracking to pick up some Enigma packets that I could get now that I had the proper gadget to get them. I go into the sewers, go down that elevator, proceed through the sewers, pick up the packets, start going back the way I came, and find that the elevator had apparently gone back up the shaft, making it impossible for me to get back up there. I reloaded the checkpoint a couple times, didn't work. I was about ready to rage-quit (possibly the entire game for good) under the assumption that I was officially stuck in the sewers and couldn't get back out, thus forcing me to restart the game (which would be absolutely moronic considering that you HAVE to go back into the sewers in order to get some packets that you wouldn't have access to on your first trip into the sewers).
Luckily, though, I backtracked all the way back to where you enter the sewers on your first trip to the sewers. Despite the fact that my map showed it as a dead-end with no exit, there was a latter to a sewer-lid that I could climb up and out of, thus freeing me from the stinky prison.
Other than that there's been some occasions where the combat would glitch up and the counter button wouldn't work, or Batman wouldn't start a beat-down after cape-stunning someone (and instead just do a regular punch to knock the stunned guy down and then, since I keep pressing x with the assumption that I just started a beat-down, he misses on the 2nd punch and breaks my combo).
