The Springfield Files - S8-E10
Continuity mistake: At the kitchen table, when Homer talks about getting mocked on his own birthday, they're eating breakfast. But when Marge, Lisa, Bart and Maggie all go to pet Santa's Little Helper, the breakfast has vanished.
Simpsons Spin-off Showcase - S8-E24
Continuity mistake: In Moe's spin-off, just before Barney leaves the bar, his beer glass vanishes.
Lisa's Date with Density - S8-E7
Continuity mistake: Whilst Chalmers notices the Honda symbol missing from his car, there are four holes in the corners of the leftover symbol. There is a screw in one of the holes indicating the symbol would have holes in its corners to hold it down. Later when Skinner finds the Honda symbol in Nelson's locker you can see there are no holes in the symbol.
Continuity mistake: When Santa's Little Helper is taken away by the Repo Men, the van's back bumper is first seen to have no number plate. When the van drives off, there is a number plate.
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Genesis Tub,' when Skinner is grading the universe in the tub, his clipboard changes from brown to blue. (00:17:55)
The Springfield Files - S8-E10
Continuity mistake: When the 'alien' is seen on the news, it is shown on the film Bart made coming out of the trees, but earlier on, when the alien came out of the woods, Bart is seen not holding the video camera.
Simpsoncalifragilisticexpiala(Annoyed Grunt)cious - S8-E13
Continuity mistake: During the song "Its the American Way" Snake is robbing Hans Moleman during Chief Wiggum singing and Snake's hair is blue. His hair has always been a brown-red color. In the very next scene to confirm its a mistake you see him in the park saying "Yo Sherry Bobbins" and his hair is back to its brown-red color.
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.
Continuity mistake: The "Stinger" only appears on the boxing gloves after Moe passes them to Homer. It is not there in all preceding shots.
The Secret War of Lisa Simpson - S8-E25
Continuity mistake: When Lisa climbs to the top of the Eliminator, there is a platform for her to stand on. Strangely in the next shot Lisa is standing on nothing so she appears to be standing in mid-air.
Continuity mistake: When the Simpsons are driving to Cypress Creek the arrangement of luggage on the roof of the car changes depending on their stage in the journey.
Lisa's Date with Density - S8-E7
Continuity mistake: The hole in Nelson's locker increases in size.
Continuity mistake: When the angry mob smash all the statues and the fountain before the song, during the song you can see all the statues and the fountain intact.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing And I", Bart discovers he has a scar where he was separated from Hugo. During the attic scene, it disappears. (00:04:40 - 00:06:10)
Continuity mistake: The extension cord Jimbo is using for a belt disappears after they run around the corner of the corridor whilst chasing Bart.
Continuity mistake: When Homer is walking and talking with Hank Scorpio when he first arrives at work there is reversed "J" on Homer's tie that comes and goes between shots.
Continuity mistake: When Marge goes to see Belle at the Maison Derriere she sits down with her.At first there is a white ornament on the small table in front of them but then at the end of the scene it has vanished.
Continuity mistake: During the big song near the end, there is a birds eye view of everybody outside dancing and singing, and Krusty, Chief Wiggum and Skinner are there outside with everyone. But in the very next shot, they all appear out one of the windows, singing a line to the song.
Simpsons Spin-off Showcase - S8-E24
Continuity mistake: In the beaver sketch, "Lisa" is holding Maggie in front of her to show everyone her first tooth. In the next shot, Maggie is instantly to her side.
The Secret War of Lisa Simpson - S8-E25
Continuity mistake: The vehicle they are driving changes form when they drop off Bart at military school to when they drive home. They leave with Homer's purple car (obvious from the crumpled headlight) and as they leave the military school it's Marge's orange car (obvious from the ski racks and lack of a trunk). It's clear from the entire scene that this is all one trip.
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