Continuity mistake: When Bart and his friends are making copies of the photo of Homer, the banner across the copier says "Copies 5 cents," but when they go to deposit the money it says 10 cents.
Continuity mistake: When Homer and Bart are at the cabaret show, Mr. Burns and Smithers are there with two women. In almost all of the shots there is a woman sitting between Burns and Smithers, except in the close-up of them when Burns asks "How does he DO it?". Then Smithers is shown as sitting right next to Mr. Burns. (00:21:00)
Continuity mistake: When Marge kicks Homer out he turns away from the door. When she slams the door he is now stood facing it completely. (00:12:40)
Continuity mistake: Milhouse makes a copy of Bart's photo for a brown skinned boy, but the boy's skin turns yellow when his father scolds him. (00:09:40)
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