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.
Continuity mistake: When Lex breaks the wall of Arkham to let Joker out, the view from inside the room shows him just a few feet away from the hole. But in the wide shot when Joker is walking out, Lex is a much greater distance away from it. The distance is too great for him to have just decided to step back for some reason.
Continuity mistake: After taking out Joker, a police officer thanks Batman for the help. Robin says he was a part of this too. There is a police car just beside Batman, and the cop is right in front of him. It then switches to a high angle before Robin finishes his statement - suddenly the cop is gone, and the police car has changed positions, now driving away from Batman.
Continuity mistake: When the award ceremony begins, Bruce exits his limo and places his arms around two girls' shoulders. His arms are stretched out around their shoulder area plus you can see part of his arms just past the girls' necks so his arms are definitely around their shoulders. Yet as the camera is behind Bruce, his arms are now lower down around the girls' backs.