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)
Revealing mistake: When Cissy is at the piano as Buffy sings and dances for Uncle Bill, only her arms move up and down instead of across the keys, indicating that's it's an off-camera person actually playing the tune. (00:16:30)