Continuity mistake: After Batman rescues Vicky he has a voice remote for the Batmobile. As the car approaches he orders the car to stop by speaking into the remote and then lowers it to his side. When the camera shot changes showing the car stopping right in front of him, he is still holding the remote to his mouth. (01:09:20)
Continuity mistake: When Joker is at the top of the building and taunting them, his chin is red (presumably from his blood when Batman socked him in the jaw.) After he falls off the building, and we see him lying on the ground, his chin is not covered in blood like it was before. (01:50:45 - 01:54:35)
Continuity mistake: When the "automated" Batmobile is sent into Axis Chemicals to blow it up, six of the Joker's men are shooting at it before it explodes, killing or seriously injuring everyone. Three of these same henchmen are also on the Joker's parade float at the very same time or very shortly afterwards in Gotham Plaza and one of them flies the Joker's escape copter at the end of the movie.
Continuity mistake: Harvey Dent is on the telephone while smoking a cigar that is partly ash. Two camera angles later he is smoking a brand new cigar with no visible ash. (00:58:25)
Revealing mistake: When the Joker is having the party with all the balloons, Vicky Vale tries to escape from the gas by getting into a car. If you look at the back window while she is driving off, the window is rolled down, which would have led to her death, not to mention motor vehicles are not air tight to begin with.
Continuity mistake: At the beginning of the movie when the police are standing outside of Axis Chemicals, Eckhardt has very distinct facial hair. In the next shot when they are inside the plant he is clean shaven. (00:23:05 - 00:24:10)
Continuity mistake: At Axis Chemicals, Jack's face is cut by broken glass and has blood gushing out of it. But in the next shot, Jack (probably the stunt double) does not have any blood on him as he goes over the edge of the rail. (00:29:00)
Revealing mistake: When Jack and his goons are breaking into Axis Chemicals, there's a scene where they're cutting the lock off of a safe. When the safe door is opened, you can clearly see that there is no locking mechanism in the side of the door.
Plot hole: Right after the Joker goes into the cathedral with Vicky, Batman follows him with no one else entering in between the two parties. How then did Joker's goons get to the top of the cathedral before Batman or the chopper? They couldn't have planned it since Joker had to tell them where to pick him up, and they didn't know he would chase after Vicky to that particular location.