Revealing mistake: When Clayface disguised as Joker is holding Talia hostage in the movie theater, they are both standing on stage in front of the screen with a movie playing. However, they are not casting shadows on the screen. Also, no shadow appears on the screen when Clayface takes on his true form.
Plot hole: The side mission "Fragile Alliance" has Batman helping Bane destroying containers full of Titan. After destroying the containers and returning to Bane, a small fight ensues followed by a cut scene of Batman trapping Bane. Bane has the drug Venom visibly going through his body the whole time so he could easily break out, but remains trapped through the rest of the game.
Other mistake: In the side mission "Identity Thief" Hush leaves Arkham City after revealing he now looks like Bruce Wayne. Problem is how he's able to, especially with Penguin's reward for bringing Bruce Wayne to him.
Suggested correction: Hush is a resourceful man, and could figure out a way to disguise himself or get to his escape route with minimal contact with anyone else. Plus, the Penguin's gang was decimated and Arkham City thrown into chaos during the events of the story, so most of the inmates probably had bigger problems than chasing a bounty that was likely rendered moot when Batman imprisoned Penguin midway through the story.
Other mistake: When Hugo Strange tells Batman about his plans to eliminate criminals everywhere, he gets stabbed in the back and through the heart by Ra's Ah Ghul. However, no blood appears on Ra's sword and there's no hole in Strange's coat.
