Continuity mistake: Bart's 1st grade drawing of cat on the fridge changes across the episode, especially its ears and whiskers. (00:04:50)
Continuity mistake: In the old main title sequence, when Homer gets out of his car, the door inside the garage is red, but when he is screaming and running towards it, it's now brown. (00:01:40)
Continuity mistake: When Bart crashes at the social club, his skateboard changes position between shots. (00:05:30)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer finds out that he has no Christmas bonus the background behind Marge is the kitchen, but then it cuts to Homer and the background behind him is the kitchen too. (00:08:20)
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."
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)
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: At the end, the barriers outside the tavern change position. (00:21:00)
Continuity mistake: During the Itchy and Scratchy cartoon, things change about the positions of the cats, the clothing, etc. (00:07:55)
Continuity mistake: When we first see the papers on top of Skinner, the jar of preserves is not visible anywhere. It is beside him in the next shot. (00:19:15)
Continuity mistake: Bart's bruised eye has healed by the time he reaches Skinner's office to lick envelopes. (00:02:40)
The Call of the Simpsons - S1-E7
Continuity mistake: When the bear first confronts Maggie, she is on a path. Yet in the next shot when the bear lands on the ground, she is on grass. (00:11:15)
Continuity mistake: When Bart is explained the answer RDRR, there is a shot of him. There is a blue background where the classroom should be.
There's No Disgrace Like Home - S1-E4
Other mistake: When Homer is at Moe's, there is a boxing match happening on TV. There is a bald guy who is getting considerably battered by the opponent and gets knocked out, and then for some absurd reason he is victoriously standing and smiling as if he had won.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer and Flanders drop their presents, the presents move around and change colours between shots. (00:10:20)
Tree House of Horror XII - S13-E1
Continuity mistake: In the end credits when the stars exit the caravan, there is a wooden step under the door of the caravan. However, when they climb into Pierce's car and drive off, the wooden step is gone. (00:20:55)
Realty Bites - S9-E9
Continuity mistake: When the real estate team learn that Marge has sold the murder house, Marge is wearing a red blazer but in the shot which faces Marge's back the blazer is missing, then in the next shot Marge is wearing the blazer again.
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