Continuity mistake: At the end of the Capital City number, where the car comes towards camera before they shout "Capital City, yeah", watch Marge's dress. It's green as the car approaches, but as soon as it parks, it turns red, right before your eyes.
Bart vs. Lisa vs. the Third Grade - S14-E3
Continuity mistake: When we first see Willie standing by the Black Wall of field trips, the latest entry is at Willie's eye level. But when the angle changes, there are a lot more names on the wall, making the last entry appear just by Willie's chest.
Continuity mistake: The stocks that are put on Marge and Homer are fitted so that their head and hands are secured and cannot be removed. Whilst in Flanders garage and Homer is using the rotary saw to remove Marge's stock, Homer's stock is still secured on him but his arms and shoulders are through the stocks.
Continuity mistake: When Homer and Marge are on stage with Brad Goodman, Homer is eating toffee apples. He keeps eating them but they stay the same size.
The Last Temptation of Homer - S5-E9
Revealing mistake: Just before Homer drives backwards into the trout hatchery, when Homer turns the key it is obvious that it is repeated footage of Marge turning the key because the hand is a lot thinner.
One Fish, Two Fish, Blowfish, Blue Fish - S2-E11
Audio problem: In this episode Homer makes a tape for Maggie because he believes that he is going to die. However the speech is terribly out of sync with Homer's mouth movements.
Fat Man and Little Boy - S16-E5
Continuity mistake: During the scene when the toys are talking about insurance, the design on the arm of the blue jacket changes in different shots. (00:04:00)
Continuity mistake: At the beginning of the episode, the school is a light purple colour, yet near the middle of the episode, the school turns yellow. (00:00:50 - 00:12:20)
Lisa vs. Malibu Stacy - S5-E14
Continuity mistake: During both conversations Lisa has with the real Stacy (the creator of Malibu Stacy), her drink magically refills itself a number of times.
Catch 'em If You Can - S15-E18
Continuity mistake: When Bart, Lisa, Homer and Marge are on the ferris wheel near the end, we can see in one shot the person behind Lisa has blonde hair, and then in the next shot the person has black. (00:18:45)
Revealing mistake: After Apu and Manjula go by in horse and cart everyone returns into Moe's. When they walk in they just disappear into a brown wall which is where the inside of Moe's should be seen.
Continuity mistake: Bart's magazine appears in the second shot of him and Lisa talking, it's not in the first.
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: During the 'Next week, on the Simpsons' clip, Maggie changes where she sits at the table. Lisa also changes where she sits, as you can see in the background. (00:21:45)
Moaning Lisa - S1-E6
Continuity mistake: When Homer and Bart are playing video boxing for the first time, the interior of the living room keeps changing. (00:06:00)
Continuity mistake: In the beginning, Bart's bedroom's window faces the backyard. When the bus leaves, it faces Evergreen Terrace. At the beginning of Bart's nightmare, it faces the backyard again. (00:00:55 - 00:15:45)
Audio problem: When the family are about to enter the Knowledgeium Homer says 'Will there be beer?' but his lips don't move.
Continuity mistake: When Bart is training up his army, the colours of the kid's tops keep changing between shots.
Some Enchanted Evening - S1-E13
Continuity mistake: When Bart and Lisa ask Marge for food while she's waiting for Homer the time on the clock keeps going back and forth.
Mr. Lisa Goes to Washington - S3-E2
Continuity mistake: When Lisa approaches the Abe Lincoln statue, there is an old person near her. In the next shot, there are three people suddenly surrounding her. (00:15:05)
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.
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