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.
Revealing mistake: While Patty tells Selma "Look who's talking" after Homer debuts his new haircut, both of their chests up to their necklaces are the same color as their dresses. Selma's dress also suddenly has sleeves on it.
Revealing mistake: When the man with the white helmet and flashlight asks Homer if he's holding on to the can in the vending machine, a large scratch appears near the upper right corner of the screen over the man's helmet.
Burns Verkaufen der Kraftwerk - S3-E11
Revealing mistake: When Homer takes out the dollar bill from his back pocket right before he puts it into the vending machine, the left side of the screen is cut off a little. You can tell especially with how the trash bin in the bottom left has a splotchy white line next to it. (00:02:20)
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.
Revealing mistake: When talking to the doctor about using his health insurance, Homer's hairline above his ear vanishes in a shot then reappears.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: When Homer brings Santa's Little Helper home, a single frame of Maggie falling off Marge's lap is misplaced.
Audio problem: At the gorge, Nelson says, "Where is he? I thought he said noon!" But Milhouse's mouth is also accidentally lip synced to Nelson's dialogue.
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)
Plot hole: Warren's (as Bob) face falls off and tries to hold it with his hand. When he appears in the next scene, his face is totally sealed with nothing to seal it with. (00:16:25 - 00:17:55)
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)
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