Continuity mistake: When the Batmobile pulls up to the theater where Tut's henchmen are emerging, Batman challenges them while standing at the open driver's side door. You can see his left hand closing the door, as well as hear it click shut - but in the next, reverse angle shot, as he and Robin leap into the fray, the car door is standing wide open again.
Continuity mistake: Lila comes through the bead curtain with the poison lilacs wrapped in green tissue paper. She drops the flowers, and in the next shot of them on the floor, the blooms don't even remotely resemble the ones she was just carrying - and the green paper has disappeared altogether.
Continuity mistake: The Batmobile returns to the Batcave by remote control. It's facing left when we get a brief, three-second shot of Batgirl talking to Batman and Robin. In the very next shot, the Batmobile has instantly turned itself around and is facing right. Its turntable (which was actually pushed manually by stagehands under the platform) didn't work quite that fast.
Continuity mistake: After Batman has captured the last fruit fly, he goes to put the vial away in his utility belt. In the close up shot, his hands move toward the left side of the belt. The shot changes to a long view and his hands are now instantly coming up from the right side of his belt.