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.
More mistakes in Batman: Arkham City
Batman: It was all a lie. There's nothing wrong with you.
Joker: Nice of you to say. But you of all people should know there's plenty wrong with me.
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: How did Hugo Strange find out that Bruce is really Batman?
Answer: Listen to the fourth Riddler interview tape. He did a psychological profile of Batman, then picked among candidates as to who could be Batman. He's also smart enough to realize only a rich man could afford all of Batman's gear and vehicles.