Continuity mistake: When the flashback of Ned and Todd Flanders singing in the Simpsons' doorway, Homer says he could use a TV tray. Then it goes back to the present time and Homer picks up a beer from the TV tray which is next to the couch. The TV tray was never there at any other point in the show. (00:10:40)
The Secret War of Lisa Simpson - S8-E25
Continuity mistake: When Lisa and Bart are practising for the 'Eliminator', Lisa doesn't have a rope round her waist, but when she falls she does.
Lisa on Ice - S6-E8
Continuity mistake: When Lisa throws her academic alert into the trash, she jumps half way across the stage without taking a step.
Much Apu About Nothing - S7-E23
Continuity mistake: When Homer comes home with Apu, Lisa closes the book she's reading and slides it to the side on the sofa. When she stands in the next shot,the book has gone.
Simpsoncalifragilisticexpiala(Annoyed Grunt)cious - S8-E13
Revealing mistake: When Dr Hibbert is examining Marge's hairs (and I think another time in the episode), some holes are too low and you can see through her head.
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: The jagged piece of metal that Homer pulls from his arm disappears from the bedside table in the very next shot. (00:16:30)
Other mistake: When Marge sees the letter from Homer, she says "You won't see me again until I'm a man." On the paper though, it reads 'But you will not see me-' and the sentence is cut off, and the rest of the paper is blank. (00:16:10)
Springfield Connection - S6-E23
Continuity mistake: When Marge is making celery soup, The Front view of her shows just the chopping board in front of her. Then when Lisa talks to her the microwave is seen in front of her.
Continuity mistake: When Nelson is handed the knife by his two friends, Martin, Bart and their cars have disappeared for two shots. (00:13:45)
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)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: At the very end of Part 1, Homer changes position between shots, and when Flanders wants a huge castle, it suddenly changes back to his normal house. (00:08:30)
Continuity mistake: In the scene where Homer decides he wants to stay with Lurlene, she locks the door about 3 times before going to kiss Homer, but when Homer leaves, he just opens the door, he doesn't unlock anything.
Continuity mistake: The "dummy" in the episode changes consistently from a real character to a dummy sometimes. When Mel jumps into the vehicle in the museum the "dummy" moves aside. When Mel shoves it out of the way, it stays in one rigid position as if it is a dummy. During the chase, the "dummy" falls on the car behind and its facial expression changes. But when one of the guys from THAT car (not the one Mel was in) goes to the dummy, its head is ripped off and you can see that it is stuffed.
Tree House of Horror V - S6-E6
Audio problem: In 'The Shinning' when the Simpsons finally arrive at the house, they climb out the car and start yelling "Hi." and "We're here." Listen to Lisa's voice, and watch her mouth. The audio is totally out of sync with her mouth movements. (00:02:30)
Tree House of Horror XII - S13-E1
Continuity mistake: In 'Hex and the City,' as they walk through Ethnictown, Marge has a handbag over her shoulder. But in the closeup when she says "Oh, listen.", the bag has gone. (00:01:15)
Realty Bites - S9-E9
Continuity mistake: When Marge finds out the Mr Hutz does real estate, the 'For Sale' sign changes from black to red and then back again.
Continuity mistake: When Krusty the Clown arrives at the beauty pageant his tie is done up. When he goes on stage it is undone.
Continuity mistake: When the Repo Man takes Marge's ring, we see the ring on her left hand. It wasn't visible in the shot before. (00:14:40)
Audio problem: In the car, when Homer accidentally kicks the horn twice, the second noise goes longer than it's supposed to. (00:08:10)
Lisa's Pony - S3-E8
Continuity mistake: When Homer tells the family where the horse will be kept, if you look in the background there are drapes on the wall. These drapes weren't visible when Marge and Homer walked in the kitchen.
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