Continuity mistake: As Lex and Joker are talking on the bridge between two towers of Arkham Asylum, Joker is shown standing in the middle of the bridge. But when the guy on the intercom announces there is an escape going on, the camera changes angles and suddenly Joker is right next to the edge.
Trivia: The opening theme to this movie is the same theme used in the 1989 Batman film, directed by Tim Burton. The opening sequence even plays homage to that film by having camera movements close up around the Batman emblem in the same fashion, and the names of the people and production team appear in the same order at the same time in the same position of the Bat symbol in both movies, most notably when the director's name appears. Funnily enough the director of this movie is named Jon Burton, no relation to Tim.
Trivia: When The Joker interrupts the ceremony and shows the video of him blowing up the building, there's a scene where he hits the detonator a few times before the building blows up. This is a scene paying homage to what happened in The Dark Knight when there was an actual unplanned delay during filming of the explosion going off during the blowing up of the hospital.