Revealing mistake: During the fight in the museum, one of Catwoman's henchmen slams into the wall beside a window. The set wall buckles and caves in, leaving the bottom edge of the window bent and jutting out. A few shots later, though, both wall and window have repaired themselves.
Revealing mistake: When Bruce, Dick and Aunt Harriet get into what's supposed to be an elevator, there's solid concrete under the sliding doors where there should be a break separating the lift car from the building's floor. It's visible again in Part 2, when Batman and Robin use the same elevator.
Revealing mistake: The crowd scenes during what is supposedly a Gotham City University student protest rally are inserts of rather blurry old stock footage. Not only is the mob far too large for a mere college rally, the footage is in black & white, while the rest of Batman is in color. Bit of a dead giveaway.