Continuity mistake: At the end, we see Krusty stood next to Mr. Burns. However, as the camera pans over the crowd he has vanished. (00:20:30)
Continuity mistake: Lisa's posture changes at the breakfast table as Bart talks about the school bus. (00:16:10)
Continuity mistake: The position of the street lamp Bart skates into changes between shots. Notice the lines in the pavement. (00:08:20)
Audio problem: When Jimbo says "Yeah come on Bart" his mouth doesn't move to start with and then makes weird motions rather than mouthing words. (00:09:45)
Continuity mistake: When the car pulls up by the theatre, you can see it through Bart's window. As the car drives off it's now trees outside his window. (00:08:00)
Continuity mistake: When Marge is telling Homer off about staying in the car she has gloves on. Camera changes to her saying "Move it" and now her glove has disappeared. Her hand also moves from being on the door to pointing. (00:05:00)
Continuity mistake: When Bart hits the streetlight while skateboarding, the streetlight is blue when he hits it, but turns grey as he lies on the floor. (00:08:50)
Continuity mistake: During the theater scene, the man in the back with the moustache and green jacket watching the Space Mutants movie changes from having yellow skin to brown skin after Bart blows a raspberry. (00:09:30)
Revealing mistake: The blonde woman's midriff (from the Space Mutants movie) flashes pink for a frame.
Continuity mistake: When Bart returns home while Lisa is watching Krusty, the door opens without Bart even touching it. (00:22:00)
Revealing mistake: When Barney says "How long will the story take?" after Bart offers to tell the mob his story, the upper half of Barney's face starting from his nose is a darker shade of yellow than his lower half. His shirt also changes colour. (00:01:40)
Revealing mistake: In the beginning, when the angry mob is chasing after Homer and Bart, there are two Dr Marvin Monroes. One of them is behind Mrs Krabappel and the other is next to Grampa Simpson. (00:01:40)
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