Continuity mistake: Wolverine first enters the sewers by ripping away a fence in the subway. When Jubilee and Gambit follow him, the fence is still intact. When they get closer it is torn again. Odd, really, because on the whole this show has few continuity errors, like self-mending clothes in other cartoons.
Heart of Ice - S1-E3
Continuity mistake: When Mr. Freeze's henchman Johnny gets his legs frozen, he is wearing pants and shoes. Later when Johnny is inside a water tank in the Batcave in order to thaw the ice, he has been stripped down to his boxer shorts. While it's possible for Batman to remove Johnny's pants above the freeze-line by cutting them away, he would still have remnants of his pants underneath the ice, but when the ice is thawed, his legs and feet are bare. (00:05:45 - 00:08:05)
Continuity mistake: In the episode where Fester invents a fabric: When Fester lies down on the parking lot, his head is first pointing upwards, towards a car, then in the next shot he has turned 90 degrees and his head is pointing towards Norman's legs.