Continuity mistake: Lenny and Carl's seating in the auditorium changes from being down close to the stage to being higher up and further from the stage.
Continuity mistake: Before Homer begins his speech to the nuclear power plant employees, Lenny and Carl are wearing white/off white shirts with ties. After the speech, Lenny is wearing his usual green shirt with suspenders and Carl his usual gray jacket.
Character mistake: When Martin Prince supposedly represents Finland's culture for their recreation of the U.N at the Model U.N. Club Martin's outfit is not in fact a Finnish national costume. The outfit he is wearing actually resembles a traditional Sámi outfit. The Sámi people are the indigenous people living in Northern Europe. The specific style of Martin's outfit has characteristics that are more typical to the Sámi on the Swedish side of Sápmi. (00:02:15)
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: When Roofi is singing at the concert, the Roofi head on the curtain is facing the left. Later, it is facing the right.
Continuity mistake: The colour of the school changes from yellow when Martin and Bart are talking before the test to grey when Bart has spoken to Otto about being held back. (00:07:00 - 00:11:00)
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: In the title sequence Mr. Largo has a baton in his hand when conducting. This disappears as he stops conducting to throw Lisa out. (00:00:50)
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)
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).
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Marge comes home and finds Homer sleeping in bed, the alarm clock next to Homer is initially facing straight but in the next shot it is facing towards Homer.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Bart, Lisa, Maggie and Homer have finished eating their slices of pizza, there are initially four crusts left in the box. When Homer is holding the box a little later on, there are now only two crusts.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Jacques tells Marge to throw the ball at Barney's Bowlarama, you can see behind Marge there are some green seats, but in a close-up of Marge in the next shot, a red chair suddenly appears.
Life on the Fast Lane (a.k.a. Jacques to Be Wild) - S1-E9
Continuity mistake: When Jacques picks up Homer's bowling ball, you can see the ball by Jacques' right hand on the rack next to him is coloured green. When we see a close-up of Homer's bowling ball in the next shot, the ball is red.
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