Other mistake: At the finish line, the crowd are missing all their appearance features such as faces, hair etc. (00:13:50)
Continuity mistake: As Nelson crosses the finish line at the time trials, The Front piece of wood on Bart's car breaks off. It is attached to the car again in the next shot. (00:14:10)
Continuity mistake: Lisa asks Homer to go to Dr Hibbert's office, when she does, Homer's hand on the window changes places between shots. Note the vertical bars. (00:15:50)
Continuity mistake: When Homer sulks on the couch, he has a pillow under his head, which is pink. In a closer shot, the pillow turns light blue, but in another shot, the cushion has turned pink again. (00:17:10)
Continuity mistake: When Homer jumps in the car having completed the Fatherhood test and drives off to see Bart race. The car shifts from reverse to forward without Homer moving a gearstick. (00:18:40)
Continuity mistake: Patty sprays Barney with pepper spray. It disappears from her hand in the next shot. (00:18:55)
Continuity mistake: Nelson makes a hole in the Honor Roller during the finals. This hole disappears and reappears between shots. (00:20:00)
Continuity mistake: At the end, when Bart gets his trophy, Marge and Homer switch positions. (00:20:35)
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