Continuity mistake: When Bruce Wayne escapes from the United Underworld (Joker, Penguin, Riddler and Catwoman), he climbs to the top of their hideout (Ye Olde Benbow Taverne) and jumps from the top of the roof (to the water below). But in the next shot, Bruce now jumps from the edge of the roof and dives into the water. (00:54:20)
Continuity mistake: In the helicopter scene in the first 10 minutes of the movie, Batman moves down on the ladder and stops. In that first shot you can see that there are about 10-12 rungs below him. In the next shot there are only two. Shortly after he gets attacked by the shark there are now at least four rungs below him, and yet he has not made any attempt to move up or down.
Continuity mistake: When the Batmobile arrives on the pier, it's parked with its front end facing open ocean (against the orange contraption on the dock) and its tail toward dry land. But when Batman and Robin return and phone the Navy, the car has reversed direction (tail now against the contraption). It's not likely Batman would arrive back at the pier, start the car, turn it around, park in the same spot, shut the car off, reopen the doors and then make a call, only to then drive away. (00:20:10 - 00:28:15)johnrosa
Continuity mistake: As the Batmobile arrives at the pier, it turns into a parking space, one of two available between a green VW Beetle and a white station wagon. In the close-up as Batman and Robin exit the car, the spaces on both sides of the Batmobile are empty. Judging by the location of the "Moby Dick" sign at the edge of the pier, the white wagon has disappeared. (00:59:05)johnrosa