Kill the Alligator and Run - S11-E19
Continuity mistake: When Homer beats the train they are on a road, but then another train comes by and hits them right where the road was.
Continuity mistake: When Bart's army is attacking Nelson, there are a lot more kids attacking Nelson than there were training with Bart.
Continuity mistake: When the remote controlled plane crashes into the roof of the burlesque house, it is seen to hit only the side of the roof, yet when Bart goes to reclaim the plane, it is nested on the top of the roof.
New Kids on the Blecch - S12-E14
Continuity mistake: When Homer is pinching Lisa with the "jealousy bug", the sign behind him changes from a gift store to an antique store.
Continuity mistake: When Marge is watching Homer's "Margarine" music video, the coffee in her cup keeps changing.
Continuity mistake: When Homer sits down in the movie theater, all the rows are completely full, including the row behind him. When he turns around to talk to Selma, the seats directly behind him are empty. Then, when Homer turns back to the screen, the Sea Captain and Dr. Hibbert appear sitting directly behind him.
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Genesis Tub,' Lisa sits on a tooth-throne in the tub, which has red cloth draped over the arms with gold tassels around the edge. However when Bart comes to take the tub, Lisa stands up on the throne and yells "Bart, no!" In this shot the tassels are gone. (00:17:45)
Continuity mistake: When Sideshow Bob is shouting and screaming just before he is taken away in a police van, Lisa and Bart swap places right before Bart says "Take him away, boys."
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When Homer is preparing the barbecue, he is wearing an apron that says "Mafia staff apron". After he goes to pick up the lighter fluid, it reads "Maffia staff apron", and after he has lit the barbecue, it is back to saying "Mafia".
Lisa's Rival - S6-E2
Continuity mistake: The position of Ralph's Star Wars action figures changes the two times they show his diorama.
Continuity mistake: When there is a zoom in of the house just before Bart gets up late, it has the old arch-shaped windows, but in the rest of the episode it has the normal windows. It's obviously a screen from Season 1. (00:06:00)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: During the family's breakfast, in most shots Marge sits right beside Maggie's highchair, but in certain close-ups they are quite a few feet away from one another. (00:05:25)
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: The shot glass that Burns places on his desk disappears for several frames before reappearing. (00:05:45)
Continuity mistake: When we first see Homer feeding the can to the goat the background shows a wooden coop. In the next shot, a purple tree stump appears there too.
Continuity mistake: When Homer shows his "incriminating photos," you can see that in them, he is bald. We know from several previous episodes that Homer had hair when Bart was a baby. He even has a bit of hair when Lisa is born.
Continuity mistake: At the end, the barriers outside the tavern change position. (00:21:00)
Continuity mistake: The bible that Reverend Lovejoy returns at the library is bigger in the first shot.
Continuity mistake: At The Town meeting Mayor Quimby's tan disappears in the middle of the scene.
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: In the bar, before Bart stomps on Mr. Burns' foot, his back is toward Smithers, but in the next shot, his back is turned toward everyone else. (00:19:15)
Moaning Lisa - S1-E6
Continuity mistake: When Homer says "I can't concentrate with that infernal racket", the shot goes up onto Lisa's room. From the outside, there is no window frame on the window. But from the inside, there is one going right through the middle.
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