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.
Mr. Freeze: You will bring me Nora or you will die.
Trivia: At the theater Clayface is watching "The Terror" a movie starring Jack Nicholson, who played the Joker in 1989's Batman.
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Suggested correction: More likely, this is a reference to Clayface's origin in the comics, where he was an actor who starred in a film called "The Terror," then dressed as its killer and killed the cast and crew of a remake set to be made without his involvement (his shapeshifting powers coming later into his character's life). This is evidenced by how the film on the projection screen appears to be a black and white film from the 30s-40s, matching Clayface's first appearance in comics.
Question: Why didn't Batman just contact Gordon and tell him what was really going on in Arkham City? They could use that against Professor Strange and stop Protocol 10 before it even began.
Answer: Because Batman didn't know until it was too late, and there was interference as he spoke to Alfred, if you remember hearing that. So contacting Gordon would've been even harder.