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: After Marge bites the candle down to a smaller size, the candle turns back to its original size for a frame.
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. (00:03:40)
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