Continuity mistake: As Martin reveals his Honor Rollor at the time trials, we can see Bart on the right side of the screen. He suddenly appears beside his car in the next shot. (00:13:00)
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: 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 helps Bart with his racer, the wall of the inside of the garage keeps changing from blue to red. (00:11:45)
Continuity mistake: When Homer calls the Fatherhood Institute about his poor test results, the guy is holding a cup with 'Super Dad' on it. In the next three shots the cup has jumped to being on his desk. (00:08:50)
Continuity mistake: At the Institute, the clipboard Dave is holding repeatedly switches arms between shots. It also disappears entirely. (00:09:35 - 00:10:35)
Continuity mistake: Patty sprays Barney with pepper spray. It disappears from her hand in the next shot. (00:18:55)
Continuity mistake: In the video store, right after Homer picks up the tape, Maggie switches arms. (00:06:05)
Continuity mistake: When Dave gives Homer the Bill Cosby book, the cover is light blue. When he reads the book in the garage, it is green. (00:09:40 - 00:11:30)
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: 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)
Other mistake: At the finish line, the crowd are missing all their appearance features such as faces, hair etc. (00:13:50)
Continuity mistake: In the garage Homer rolls up one sleeve but in the next shot both are rolled up. (00:10:35)
Continuity mistake: When McBane's partner asks him to do just one thing for him, the picture keeps appearing and disappearing from his hands. (00:05:30)
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