Continuity mistake: After the "sponge incident," Bart is standing in the drive with the sponge packet in his hand. In the next shot he says "everything about me must go," but the packet has vanished from his hand.
Continuity mistake: After Moe yells at Ralph, there's a woman in the background staring at Moe with an angry look on her face. She turns her head away from him after some seconds, but in the very next shot, she is looking at Moe with the same expression on her face.
Continuity mistake: When Milhouse snitches on Bart, Martin has grey hair and a black suit. In the very next shot he has his ordinary hair and is wearing a brown suit.
Continuity mistake: Jasper's beard is missing when everyone is singing "In-A-Gadda-Da-Vida" at church.
Continuity mistake: When Moe tries to convince Dr Hibbert that Moe's is a family restaurant, Carl's skin is yellow.
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