Surf's Up! Joker's Under! - S3-E10
Other mistake: An amazingly precognizant Dick Grayson is already wearing his surfing togs before Commissioner Gordon calls to say that Joker has invaded the surfing community. (00:04:30)
Suggested correction: Dick isn't amazingly precognizant. He's wearing swim trunks while using the rag to prep his own surfboard. Barbara Gordon was already at the beach with Skip, and Dick is heading to the beach with his surfboard as well (00:04:34).
The Joker's Hard Times (2) - S2-E38
Continuity mistake: The Batmobile pulls up in front of the Platter-Porium, and you can see that only Batman and Robin are inside the car. When the shot cuts to close-up, though, Venus is sitting in between them. (Tight squeeze: it's a 2-seater and she must be straddling the transmission hump and hand brake - ouch.) The shot cuts back to full for them to jump from the car, and Venus has disappeared again. (00:13:40)
Suggested correction: We do see Venus in all three shots. When the Batmobile pulls up in front of Platter-Porium, in the first wide shot we see blonde hair between Batman and Robin. Then after the closeup, in the second wide shot (same angle as the first) when Batman and Robin have exited the car, we see Venus turn and poke her head out of the Batmobile, on Robin's side of the car. Also, in the closeup when Batman opens the door, we see Venus is sharing the passenger seat with Robin, directly beside the transmission hump and hand brake, so no ouch for her. Venus does the same thing in the next episode, when she's brought to the Batcave.