Continuity mistake: Towards the end of the gunfire exchange scene at Axis Chemicals - from the point at which Joker was pondering an escape on the catwalk until Batman turns around to see the shadow of a police officer closing in on him - notice how the exit bears an altogether different appearance between views. (00:27:35 - 00:29:40)
Revealing mistake: When Jack falls into the chemical vat it's obvious the vat is quite shallow as he doesn't actually sink into the chemicals but instead just kind of lands and then sits there as liquid splashes out around him. To top it off, the subsequent shot of him disappearing into the chemicals is reversed as several bubbles can be seen 'unpopping' and growing smaller.
Continuity mistake: When Batman and Vicky are running from Joker's museum plot, and are running from Joker's henchmen, he shoots a cable up to a walkway. As the camera shows him firing, he fires the rope at a 45 degree angle, yet when he and Vicky are going up on the rope, the walkway is directly above them and the rope is perpendicular to the ground.
Continuity mistake: Vicky Vale's first name is V-I-C-K-I in the credits. On the cover of the magazine, it's spelled V-I-C-K-Y.
Continuity mistake: When Batman collects the balloons' cables in his flying vehicle's anterior contraption, he gets 6 or 7 cables caught, but when he closes the scissor-like mechanism, there are only 5 visible cables. Also, when he collects them, they gather at the back of the mechanism, but when he closes it, they are neatly caught in small notches.
Continuity mistake: Whenever shots show the view looking down on the ground when Batman and Vicky are hanging from the cathedral, it only shows two spotlights shining upwards from the ground. In other shots just showing the upper part of the cathedral, there are three or four beams visible. Also, the movement of the beams from the ground and the ones actually on the actors don't correlate between shots.
Revealing mistake: When the Batjet crashes, if you pay close attention to the scale of the jet, cars and buildings in relation to the scale of the fire and explosions, it is very clear that this scene was created with models.
Audio problem: Knox is thrown from the hood of Vicki's car into a pile of garbage. He cries "No, no, no." He is obviously dubbed, as his cries continue briefly after he has already landed in the garbage.