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.
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.
Revealing mistake: Right after Joker falls off the top of the cathedral, Batman and Vicky fall too and we catch them three times before Batman's grapple digs into the stone. On the second and third time you can actually notice Vicky's face expression doesn't look one bit scared, so you know they're not falling. You can also see there's a screen in the background. (01:58:40)
Revealing mistake: When Batman drives the Batmobile into the Axis Chemicals factory, watch closely when he slams through the first gate - you can see the gate is swaying and starting to open before the batmobile hits it, indicating it wasn't really closed and was left unlocked and partially open to make it easier for the stunt-driver to drive the Batmobile through it.
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.
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.
Revealing mistake: After the Batmobile's pair of machine guns riddles a straight line of bullet holes through a bay door of Axis Chemicals, it drives in and eventually goes on to blow up the plant. It might seem like the bullet holes themselves would weaken the bay door enough for the Batmobile to push through. But instead - as the bay door falls to the ground - notice how a ready-made seam splits apart directly above the line of bullet holes. (01:34:15)