When Batman uses his bat-brass-knuckle it suddenly disappears, and remains gone, after he hit The Penguin.
During the time Robin and Catwoman are unconscious in the Batcave, the Catmobile vanishes from the turntable, is replaced by the Batmobile, and is never seen again.
During the battle atop the blimp Catwoman's mask and whip alternately appear and disappear from her person.
Circus elephants are never left with pointed tusks, as a matter of spectator safety. The tusks would be removed, or dulled and covered with protective decorations.
When Batman and Robin get out of the Batmobile in the Batcave, the turntable rotates but Robin walks straight off the platform as if it was still.
When exiting the Batcave the first time, the Batmobile turns right. In every episode of the TV series, to get to Gotham Police Headquarters, they always turned left.