Continuity mistake: In the cinema, it is clear that the people attending the movie keep on changing. For example, For a few shots, you can see that Krabappel and Skinner are sitting in The Front row, but the next time you see those seats, they have been replaced by Lenny and Carl and Krabappel and Skinner aren't in sight.
Continuity mistake: When Homer is stuck in the hole after saving the plant, Marge is seen in the background wearing lipstick. When Mr. Burns asks if there is anything he can do for them, there is a closeup of Marge and her lipstick is gone. When they cut back to Homer, Marge is again wearing lipstick.
The Old Man and the C Student - S10-E20
Continuity mistake: When Homer offers Lenny some nuts a spring pops out and gets Lenny in the left eye, but the next time we see Lenny it is in his right eye.
Continuity mistake: When Homer is threatening to boot the Prime Minister, he is holding him still with his left arm. When the shot goes to behind Homer, he has his right arm on the Prime Minister's shoulder. When the shot cuts back to a direct view of Homer, his right arm isn't touching the PM.
Little Girl in the Big Ten - S13-E20
Continuity mistake: After Lisa's dream she lines up and the girl on the bars is the same girl the teacher told to go out.
The Last Of The Red Hat Mamas - S17-E7
Character mistake: When Homer finds Marge's folder, it reads "Heist Plan: Burns Manson" instead of "Mansion" as it should be.
Continuity mistake: When Homer buys Ned's living room for $75, Bart is wearing a pink "Ned loves Maude" T-Shirt but by the end of the scene where Bart says "Hands off my china hutch." his shirt is the standard orange shirt. (00:14:40)
Continuity mistake: In the park, Marge's necklace changes from white to red. (00:15:40)
Continuity mistake: During Sadgasm's first appearance, a girl with a green skirt, a red sleeveless shirt and grey hair moves from place to place during the "concert."
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: In the scene where Marge is talking to Bart's teacher, Marge is "punished" by writing lines on the blackboard. In the first shot of her doing so she has written the line 9 times, but in the next shot there are 11 lines. (00:05:10)
Treehouse of Horror XIII - S14-E1
Continuity mistake: The beers Homer puts under the hammock vanish when the hammock breaks, and Homer falls to the floor. (00:01:15)
Continuity mistake: After Homer falls asleep at the wheel the truck starts to turn the corner. As its going around the bend you can see a white line on the road. The following shot the line has disappeared.
Tree House of Horror XII - S13-E1
Continuity mistake: In the opening sequence, when the coffins shoot out of the grave, one of them changes colour between shots, when it hits the pillar. (00:00:25)
New Kids on the Blecch - S12-E14
Continuity mistake: When Bart and the group are singing at school, when we see L.T.Smash, his arms are down then instantly in the next shot, they're on his sides. (00:08:10)
Sleeping with the Enemy - S16-E3
Continuity mistake: When looking around the course at the beginning we see there is a spinning toy, which you find in some parks, yet when Willy comes along, it has disappeared in the distance. (00:00:40)
Tree House of Horror V - S6-E6
Other mistake: At the speed that Homer was chasing the family outside the lodge at the end of "The Shinning", he would have caught them up with ease.
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: In this episode and maybe in other one, the door to the basement is at the entrance of the house, but that's a closet in other episode.
The Great Louse Detective - S14-E6
Continuity mistake: When Bob pins Bart onto the wall in the final scene, his pajama top is stretched up so you can see his stomach. It then zooms in slightly when he looks at his watch and his stomach is covered.
Tree House of Horror IX - S10-E4
Audio problem: At the end when Bart says 'Don't forget Ken Star' his mouth doesn't move.
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