Continuity mistake: When Batman and Robin are in the museum speaking with the director, Batman's chest emblem is high enough on his chest that it nearly touches the bottom edge of his cowl. In the next shot, when he leaves the museum, the emblem has moved down several inches.
Continuity mistake: After Annie drops the chandelier on them, Batman and Robin are knocked unconscious. No one's had time to move either of them, but when Andy comes into the saloon in the next shot, Robin has somehow shifted positions on the floor: he's not in the same spot or position he originally fell in. (00:21:30)
Continuity mistake: Molly is about to disguise herself as Robin. But the wig she's holding isn't even remotely the same color as Robin's hair. Of course, as soon as she puts it on and transforms herself, the wig darkens and becomes Robin's actual hair. (00:05:45)
Continuity mistake: During the fight in the art gallery, the papers on the desk to the left of the screen are scattered. But in some shots of the fight progressing, the same papers have straightened themselves back into nice, neat stacks again. (00:17:00)
Continuity mistake: When Batman starts the Bat-Turn, the parachutes are shown deploying on a 6-lane major roadway (3 lanes in each direction) in a very open area, but after completing the 180-degree turn, the car is shown driving away from the crumpled chutes on a much narrower side street among tall buildings. (00:14:10)
Continuity mistake: While the unconscious Robin is being carried away from the Batmobile by one of Riddler's thugs, his cape loosens and appears to completely fall off just before they exit the frame. In the next shot, Robin is still being carried away but his cape is securely back in place.
Continuity mistake: When the Penguin goes to Wayne Manor to put Batman and Robin to sleep with the gas from his umbrella, just before he shoots the orange gas at Robin's suit of armor, there's a quick shot of the armor's helmet. The problem is that there's already an orange stain on the face of the helmet from the orange gas that comes out of the tip of the umbrella, even before Penguin shoots any gas. (00:19:15)
Continuity mistake: Batman tosses a large white box at one of the henchmen. The box lands on the round dais of the clockworks, but as that dais begins to rotate, the box disappears. It pops back up a few shots later, now sitting on the stationary corner of the clockwork platform. But as the fight rages on, it vanishes again between shots. (00:21:30 - 00:22:10)
Continuity mistake: Tied to a conveyor belt, Batman and Robin move past a stack of boxes stenciled with the factory's name. Cut to close-up, and they're now back to a position right next to the boxes. Back to master shot, and the boxes are once again several feet away - at least until the next close-up. (00:02:50)