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.
The Joker's Hard Times (2) - S2-E38
Continuity mistake: At GCPD HQ, when Commissioner Gordon decides to call Batman he removes the Batphone's acrylic dome cover and lifts the red receiver, still holding it when Joker shows up. Then, when Joker announces his next target is Libra the scales, in the next shot from a different angle, the Batphone is now untouched under the acrylic dome, between shots. (00:02:55)
The Joker's Hard Times (2) - S2-E38
Continuity mistake: After Joker enters Commissioner Gordon's office, Gordon and Chief O'Hara walk over to the window, and the Batphone table is behind them, beside Gordon's desk. Then Joker makes two "quick-frozen cops" and runs off to snatch Justice, leaving Gordon and O'Hara immobile. When their shock paralysis wears off, Gordon and O'Hara rush over to Gordon's desk, but the Batphone table and the Batphone have vanished (note the rug's pattern). (00:03:00 - 00:04:55)
The Joker's Hard Times (2) - S2-E38
Continuity mistake: When the Joker directs Gordon and O'Hara to look at the statue of Justice, they look at it from a front view. But when Joker comes out of the Police building where he left them frozen, it's from behind the statue, rather than in front.