Continuity mistake: When Sherri and Terri raise their hands and say "like us Mrs. Krabbapple" they raise their hands over their heads. Camera cuts and their hands are a lot lower. (00:04:20)
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: In Homer's flashback, when the pimp chases Homer, who is covered in garbage, Homer runs away from him on one side of the street. When Homer runs on the other side of the street, he is not covered with garbage. When he climbs a ladder and falls into a manhole, he is covered with garbage again.
Continuity mistake: When the teacher is looking out of the window, Bart has his paper in front of him on the desk. The paper disappears in the next shot, but reappears when Bart takes Martin's paper off the table and puts it on his desk. (00:06:10)
Tree House of Horror V - S6-E6
Continuity mistake: In "Nightmare Cafeteria", a teacher walks into the classroom and sees Bart sitting at his desk facing backwards. At this point, you can see the lockers behind the teacher are white, but in the next shot they are blue.
Tree House of Horror V - S6-E6
Continuity mistake: In "Nightmare Cafeteria", when Bart is being served his lunch at the lunchroom, his tray is initially plain but in the next shot it is now divided into six squared segments.
Tree House of Horror V - S6-E6
Continuity mistake: In "The Shinning", Homer is eating a bag of crisps while sitting on the sofa and you can see "Potato Crisps" logo on the bag is coloured red, but in the next shot it is now blue.
Continuity mistake: The comic book guy should be seen on the ground when Bart comes to the music store, but he has disappeared.
The Lastest Gun in the West - S13-E12
Continuity mistake: At the start of the episode, the dog eats Bart's clothes through the letterbox, but a minute later, when the dog next comes to the house and Homer opens the door, there is no letterbox.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: Dr. Hibbert's clothes keep changing during the song near the end. He goes from having his white lab coat, a blue sweater, then a pink sweater.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: During Homer's flashback, Homer passes the sign that says "Jeremiah's Johnson" twice.
Brother From Another Series - S8-E16
Continuity mistake: Ruth Powers' hair is red in one of the shots of the protesters. Her hair is brown in other shots of her.
Continuity mistake: In the shot before Nelson says "Hey, Simpson. Race you", Ralph is seen sitting on the row in front of Martin. But when Ralph says "Go, banana" he is suddenly sitting two rows in front of Martin. (00:05:25)
Please Homer, Don't Hammer 'Em - S18-E3
Continuity mistake: In this episode Principal Skinner breaks into Bart's doctors office to find out if Bart has a 'kryptonite'. Bart discovered Skinner was allergic to peanuts. On Bart's medical history form under 'known allergies' it has shrimp ticked (they later battle with shrimp and peanut on a stick). However in a previous episode (The Heartbroke Kid, season 16 episode 17) it was discovered that he was allergic to cauliflower, so that should have been on the list as well.
Continuity mistake: Millhouse's hair color changes from when we first see him to when Bart comes back to the school yard.
Continuity mistake: In the surgeon's office there are three certificates on the wall with ribbons on them. In the first shot there are two red ribbons and a blue one but in the shot where Homer stands up to read the bill all the ribbons are red.
Continuity mistake: After the boy's car gets crushed, Bart sells Milhouse's glasses for $600. Then Milhouse knocks over the Coke bottles and the clerk gets the money back and keeps the glasses. The next scene, where they try to get on a train that goes to Springfield, you can see Milhouse in his glasses and throughout the rest of the episode.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: When Bart and Lisa find the record Melvin and the Squirrels, they hand it to the Comic Book Guy to play. While the record is in his hand you can still see it displayed on the rack.
Love, Springfieldian Style - S19-E12
Continuity mistake: In the third story of the episode, Bart and Nelson throw Martin into the Jukebox despite it never being opened. When he is trapped inside the box the glass is firmly in place as well.
Continuity mistake: Near the end when Homer is going into the show, he is not holding his coat. Then it appears in his hands and gets stolen. In the very next scene, he then wears his coat again. (00:19:40)
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