Other mistake: When the Joker fires a missile near the end of the movie it curves to the left. The writing on the missile is backwards, showing that it is reversed footage from earlier in the film, when it curved to the right.
Other mistake: The scene where the Penguin is dehydrating his henchmen. Watch as the last henchmen is dehydrated - the shot changes to the Penguin and the Riddler. You hear the Riddler's laugh but his lips don't move until the end of the laugh.
Other mistake: When Penguin and the others attack Bruce on his date in his hotel room, Penguin is the first one to charge him. Bruce takes a swing at Penguin's face and he goes flying from the blow. You don't even need to slow the film down to see that Bruce totally misses him.
Other mistake: When the Batboat is approaching the submarine before the final fight, the shot from the periscope is an overhead shot, not a surface shot like all the others in the film.
Other mistake: If you look closely at the top left part of the screen, you can see Penguin hit Robin with the umbrella and turn to the zip line in a far shot of the fight. One shot later, just after Batman kicks a pirate off the side of the sub, the same act is repeated when the camera is focused on the two of them.
Other mistake: When searching the buoy for clues, Batman goes to take out an obvious screw that was supposed to hold on the panel hiding the projector. The screw is located in the top of a seam where two panels were riveted. After removal, the panel is removed and you can see the seam again that would have been hidden by the panel, as it was tall enough to fit the side from the walkway to the top. Also, the lenses on the projector were obviously fake. Any projector with lenses that badly chipped and faded would have been repaired or replaced. In addition, Batman is supposedly loosening the screw, but was turning the screw to the right, which would be tightening it.
Other mistake: After opening the abandoned elevator, the Penguin tells his cohorts to hold their breaths because of lingering gas, and there was no real sign of it. However, before the elevator, there was colored gas all over, and he walked through with no ill effects, and held his breath with the others.