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)
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 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: The position of the street lamp Bart skates into changes between shots. Notice the lines in the pavement. (00:08:20)
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)
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: Lisa's posture changes at the breakfast table as Bart talks about the school bus. (00:16:10)
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: When Bart returns home while Lisa is watching Krusty, the door opens without Bart even touching it. (00:22:00)
Revealing mistake: The blonde woman's midriff (from the Space Mutants movie) flashes pink for a frame.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Lisa is speaking to Bart in the kitchen at the start of the episode, Lisa's hands are on the kitchen top. In the next shot, they aren't. (00:00:25)
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: At work, the salad in Homer's sandwich disappears when he mentions that 'she' made it.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Jacques is trying to seduce Marge at Barney's Bowlarama, the ball he is holding is coloured purple. When we see him a little later on, he is now carrying a green ball.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Marge is on the phone to her sisters, her necklace changes from white to red.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: Near the end when Homer is putting the colored ball things in the tube, right before Marge comes up behind him, the stripes on his tie switch sides for one shot.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Marge is making peanut butter sandwiches in the kitchen, she has already made one sandwich and there is one slice of bread by the peanut butter jar. When Homer walks up to Marge, another slice of bread appears.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Bart is eating a doughnut when talking to Lisa in the bus, the apostrophe on "Comic's" in his bag keeps disappearing and re-appearing between shots.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Marge reads Jacques' bowling ball, it says "Brunswick." Later on in the episode, it reads "Jaques" (spelt incorrectly).
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