The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: When Marge is speaking on the phone to her sisters, her sisters say something that sounds like they said that Homer is ugly. Marge then puts down the phone wire that she was curling round her finger. You can temporarily see that the phone wire disappears when Marge puts it down. It is at the very end of an early scene, because as soon as this happens it changes to another scene. (00:04:40)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: After Homer brings Santa's Little Helper home, Homer and Marge hug, and if you look behind them, the background is upside down. There is a picture hanging upside down, and there is a lamp which seems to be hanging from the ceiling. Then in the next shot, the background is normal. (00:21:40)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: When Homer brings Santa's Little Helper home, a single frame of Maggie falling off Marge's lap is misplaced.
Answer: I'm not sure if this is the one you're thinking of, but an episode of "Ray Bradbury Theatre," called "A Sound of Thunder," dealt with a similar matter: a group of hunters travel back in time to hunt dinosaurs, only to find things have changed when they get back because someone stepped on a butterfly.
Xofer