Krusty Gets Kancelled - S4-E22
Continuity mistake: When Bart and Lisa are helping Bette Midler pick up trash on the highway, Bette picks up an empty can which says Buzz Cola on it. Just as she yells, "You pigs!" the label on the can switches to Duff Beer.
Continuity mistake: At the end when Nelson's goons are holding on to Nelson, they both have brown skin. But in the next shot, one of them goes back to having yellow skin.
Continuity mistake: When Homer is rolling around on the grass outside the house with Bart, Lisa, Santa's Little Helper and Snowball II after the hair formula works, Snowball II is drastically larger than usual in the overhead shot.
Continuity mistake: During the wedding, look at the man with the blue hair carrying the tray with hors d' oeuvres that Homer is eating. When Homer says "Hey wiener boy. Where do you think you're going?" the man's collar changes from white to black instantly.
Continuity mistake: A huge fight begins in front of Mark Hamill's stage. Homer, Quimby, Hamill, Bart and Lisa escape the fight through an emergency exit right behind the people fighting. But in a shot of the five running out, the people fighting inside have disappeared.
Continuity mistake: The size of the smiley face on Krabappel's mug keeps changing between shots. (00:04:50)
Continuity mistake: Bob duct tapes Bart's mouth before telling him his story, but the duct tape disappears when the story finishes. (00:12:30 - 00:14:10)
Once Upon a Time in Springfield - S21-E10
Continuity mistake: The merchandise Krusty asks the kids to hand back doesn't appear in the kids' hands until the merchandise is taken off them. (00:01:55)
Brother From Another Series - S8-E16
Continuity mistake: Sideshow Bob's seat belt is on in one shot but gone in the next when he has been released from prison.
Continuity mistake: Bart, Lisa and Milhouse run away from the others and are stopped by a cliff. Milhouse then grabs onto a vine which was never there in previous shots. (00:19:00)
Continuity mistake: At the trial, Milhouse moves over to Lisa and Bart is in the middle of them. In the next shot, Bart has disappeared. (00:15:25)
Continuity mistake: Everyone discovers Milhouse ate the food so they walk up to him. The shot cuts and they are further away than they were in the previous shot. (00:13:50)
Continuity mistake: As soon as the fish bites Bart's butt and causes a rip in his shorts, the rip disappears almost instantly. (00:12:40)
Continuity mistake: The part of the bus that got a hole in causing it to sink changes position when Bart goes to get the cooler later. (00:07:10 - 00:12:20)
Continuity mistake: A fire is started when Milhouse's glasses are used by Nelson. But when Nelson hands Milhouse back the glasses in the next shot, the fire has disappeared. (00:11:40)
Continuity mistake: There are 10 kids stuck on the island. But after the kids have washed up on the island and it cuts to the wide shot and it shows them on the beach, there are only 6 kids. (00:07:20)
Continuity mistake: When the kids wash up on the island, Lisa, Wendell, Martin, Lewis and Sherri are on land and Bart, Milhouse, Ralph, Nelson and Terri are still in the water. In the next shot, Bart, Milhouse, Ralph, Nelson and Terri are on land with the others. (00:07:15)
Continuity mistake: The pens and pencils in the good butter change between shots when Homer begins his website. (00:04:55)
Continuity mistake: At the Model U.N. meeting, Bart finishes speaking and puts down his papers on the right hand side of his desk. Two shots later, the papers are on the middle of the desk. (00:03:10)
Continuity mistake: At the end of the episode when Bart, Lisa and Maggie greet their parents Bart says that they were in the Green Room (a room where the cast of a show can relax when not performing) and comments that '[he] ate so much shrimp!' This conflicts with the episode 'Please Homer, Don't Hammer 'Em', where it is revealed that Bart is allergic to shrimp.
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