During Batman and Joker's fight, Batman kicks out one of Joker's teeth, later on when Joker puts on his jet pack and starts to take off he has all of his teeth, but in the next shot his tooth is missing again.
Just before Batman comes to question Arthur Reeves in his hospital room, the doctor and orderlies tell him to rest and clearly slam the door. In the next shot of the room's door, it is half open. Then, immediately after Batman is seen, it is fully closed.
In the scene where Andrea is being sucked into the fan at the Gotham worlds fair, Batman rides in on his motorcycle. He turns into the fan to rescue her, but his cape is flapping in the opposite direction to the fans sucking.
During the opening sequence, the camera pulls back dramatically through the myriad buildings of Gotham City. As this occurs, the camera actually passes through several buildings - a common 3D animation problem when rendering. As a result, a few buildings "pop" into view out of nowhere.