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.
Continuity mistake: After Apu & Homer find Jasper in the freezer. Apu removes a note from his hand. Minutes later Dr. Nick walks in the door you see Jasper still holding the note then disappears again when Dr. Nick opens the freezer door.
Milhouse Doesn't Live Here Anymore - S15-E12
Continuity mistake: When Bart and Milhouse arrive at Milhouse's home, there is a red car in the driveway. When Bart screams, it has gone. (00:05:10)
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: When Homer sneaks into Maggie's room to smash the CD player, there is a yellow box with musical notes painted on it. The notes are different in each shot. (00:02:30)
Continuity mistake: When Marge's sisters start smoking in the flashback, there is only one ledge on the wall behind them. In the next shot there are three ledges and a clock. (00:04:05)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: Homer drives his normal car to the plant's parking lot. When he and Carl meet, his car has changed to being blue. (00:07:00)
Other mistake: When Bart and Homer do a test drive on their race car, it is daytime, when supposed to be night-time. (00:11:50)
Lisa's Pony - S3-E8
Continuity mistake: During Lisa's performance, In one shot of the audience we see, from left to right: Ned Flanders, Maude Flanders and some lady. The rest of the talent show showed us that Jasper was sitting where the lady was. (00:05:45)
Continuity mistake: When Lisa first discovers Jebadiah's confession, she is holding the fyffe and wearing his racoon hat, the screen fades to black (I'm guessing for the ad break) but when it comes back Lisa is standing in exactly the same position, still reading the confession, still holding the fyffe, but no longer wearing the hat.
Continuity mistake: There are two problems with Lisa's Indian burns. When we first see them, she has 4 burns. Then, while she is showing them to the bullies, there are 3, then 4 again. Then, in the very next scene when she is walking with Nelson in the schoolyard, they are gone altogether.
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When there is a queue to see the movie, it stretches right back to the Simpson house, and we see Bart looking through the window. However, when Homer talks to Bart whilst sitting on the window, the queue has disappeared. (00:16:45)
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When the Simpsons are about to eat on the spaceship, in one shot just before they eat there are 3 candles on the table, and when they all sit down they're gone. (00:10:40)
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: Just before Duff man arrives, Barney has loads of sweat on his shirt. But when Duff man pushes the big jug of beer towards him in the next shot, the sweat is gone.
The Fat and the Furriest - S15-E5
Factual error: Homer creates a giant sugar ball by making a normal sized cotton candy on a paper cone, and then coating it with liquid caramel. The cotton candy holds its shape and Homer continues to expand it with more cotton candy and caramel. However, cotton candy dissolves very quickly and tears apart easily. Between the weight and moisture content of the caramel, the original cotton candy would have immediately melted and/or collapsed.
Skinner's Sense of Snow - S12-E8
Audio problem: When Principal Skinner is watching the kids throw the books in the fire, someone goes to throw Huckleberry Finn into the fire. He says "Not Huck Finn. I spent hours crossing out the sass-back." While he says this, his lips don't sync with the words.
Continuity mistake: When we see Skinner's car before the newspapers fall on him, it is a light-brownish color. When the police arrive, it is the same color as the cop cars. (00:19:10)
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.
The Trouble With Trillions - S9-E20
Continuity mistake: When Homer is watching TV early in the episode, he has a watch on his left wrist. When he begins working on filling out his tax forms, the watch has disappeared. When he takes down the sailboat painting from the wall, the watch has returned.
Continuity mistake: When Marge and Homer are put in stocks, Marge initially has lipstick on, but in subsequent courtroom scenes it has disappeared.
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.
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