Lisa vs. Malibu Stacy - S5-E14
Continuity mistake: When the Simpsons are about to leave the house to go to the mall, they're all wearing jackets, but when they're in the car just a few seconds later, none of them have their jackets on.
Other mistake: In the scene where the Simpsons are viewing the path of the Corvair's Re-entry, the blip representing the spaceship crosses the entire US from North-West to South-East in about three seconds. This is really impossible, even for something going as fast as a spaceship on re-entry would be.
Continuity mistake: When Homer is in space, when he is about to free the ants, the crisps that he opened earlier have disappeared from the background. This type of mistake happens again when both the crisps and the ants disappear and reappear between shots.
Continuity mistake: When Barney becomes his old self again at the training center, he gets on a jetpack while holding a bottle. In the next shot while he is in the air, the bottle is gone.
Revealing mistake: When Moe grabs Ned Flanders' shirt at the bar, Ned's torso is incorrectly drawn over his arms as well as the mug he is holding. (00:10:50)
Continuity mistake: At the end of the episode in church when the group of parishioners moves forward to forgive Ned there is a woman amongst the group who has light green hair. However, when there is a wide angle shot of the group again she is nowhere to be seen.
Continuity mistake: When Homer drives his car to work it is lime green instead of the usual purplish color.
Other mistake: When somebody throws a cola can at Homer, the can never hits the ground.
Audio problem: After everyone congratulates Ned, he goes to Homer and his mouth moves but nothing is said, and the first line afterwards is not in sync with his mouth movements.
Revealing mistake: The people waiting in line for the game are extremely crude drawings. Some of them aren't even completely drawn, e.g, some are missing arms, legs and other body parts.
Revealing mistake: In one angle when the Flanders are having dinner, Ned's eyeglasses have no temples.
Continuity mistake: When Ned is saying grace, the plates on the table contain no food, but when Homer comes through the window there's food on the plates.
Bart Gets an Elephant - S5-E17
Continuity mistake: Immediately after being chained to a tree, Stampy crushes several objects (a lawnmower, a bike, a doghouse, and a trash can). In the very next shot, which comes after a commercial break, all of these objects are in fine shape. Then the shot changes again and we see them destroyed once again. (00:09:30)
Bart Gets an Elephant - S5-E17
Continuity mistake: Bart's elephant crushes the dog house, then it is shown standing, and then it is crushed again.
Burns' Heir - S5-E18
Continuity mistake: When Mr. Burns is sitting in front of the fireplace, he has his normal blue outfit when seen from behind, and a purple night gown when seen from The Front. (00:02:50)
Burns' Heir - S5-E18
Continuity mistake: When Homer and Marge are talking to Chief Wiggum, the Rubik's Cube and the cup on his desk changes to a doughnut between shots. (00:13:20)
Burns' Heir - S5-E18
Continuity mistake: When Homer says, "You idiot," to the programmer, the red ashtray changes position on the desk. (00:15:55)
Burns' Heir - S5-E18
Continuity mistake: The doughnut Homer later picks up isn't by the door when Lenny walks into Mr Burns' office, and we never see anyone put it there.
Burns' Heir - S5-E18
Continuity mistake: Hans Moleman has brown skin at the beginning of the episode and yellow skin at the end.
Burns' Heir - S5-E18
Continuity mistake: A criss-cross pattern appears on the fireplace during the closeup on Smithers after Mr. Burns told him that he doesn't have a heir.
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