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.
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.