The Joker Goes to School (1) - S1-E15
Revealing mistake: Batman drives out of the batcave alone. The first bit of stock footage of the car leaving the cave does indeed show him alone in the batmobile. But the very next stock shot of the car speeding down the dirt road shows us Robin sitting in the passenger seat. (00:05:25)
The Day Nothing Happened - S2-E20
Revealing mistake: The snowman is an obvious Styrofoam props the kids have set up in the family room, as the fake snowflakes fly right off it during the kids play, including the white patches beneath the body.