Continuity mistake: Nelson makes a hole in the Honor Roller during the finals. This hole disappears and reappears between shots. (00:20:00)
Continuity mistake: When Bart arrives at school in the bus, after Homer plowed the road for the bus, the sidewalk is covered in snow except for Martin's footprints. Then, when he gets out, the sidewalk has been shovelled, as there is no snow on it. Following this, Bart is pelted by snowballs, which sends him falling face-first into the sidewalk, which is once again covered in snow. (00:10:20)
Continuity mistake: When Bart uncovers the photo of the Simpsons behind the books in Lisa's locker, the books change between shots.
Other mistake: How can Sideshow Bob make the "I H8 BART" licence plate if there are no number keys on the keyboard? (00:04:45)
Homer's Triple Bypass - S4-E11
Continuity mistake: In this episode, Homer closes the curtain on Ned when he is praying. And the curtain is blue. However, a few scenes afterwards, when Homer is talking to Krusty, the curtain is green/beige. (00:14:10)
Continuity mistake: When Homer and Marge come home from the dinner, Marge is wearing a fancy dress. But when Bart falls out of the house right after Homer walks in, she has her typical green dress on. (00:06:15)
Continuity mistake: When Homer opens up his bar there are 4 cars parked outside, but later when Moe opens the garage door there are no cars, but no one has left.
Home Sweet Home-Dum-Diddly Doodly - S7-E3
Continuity mistake: At the Flanders' house, in the kitchen, Bart and Lisa have sandwiches on plates in front of them. The shot changes and everyone on the table has an empty bowl including Bart and Lisa.
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: As Bart is on the phone trying to book his new act, you can see there is a split down his white shirt. When the shot changes and he tells Lisa to be quiet you can see that split has disappeared. (00:15:05)
Continuity mistake: When Mr. Burns tells Smithers that Homer is the next employee of the month, his huge red chair he was just sitting in has disappeared, and Mr. Burns is in a different position. (00:10:30)
Continuity mistake: When Homer apologizes to Moe at the end, he comes in while the door is left open. It remains closed for the rest of the scene. (00:21:05)
Moaning Lisa - S1-E6
Continuity mistake: When Marge says, "Oh Homer, you'll lose your head if it wasn't secured to your neck," her necklace is white. However, when she gives the cup cakes to Homer and Bart, it is red. (00:02:00)
Continuity mistake: After the dinner with Sideshow Bob, Patty, Selma and the Simpsons, the food on Bart's plate changes between shots. We first see a piece of meat with some peas, then we see two pieces of meat and some mashed potato. It changes randomly throughout the scene. (00:02:40 - 00:07:05)
Burns Verkaufen der Kraftwerk - S3-E11
Continuity mistake: When Lenny tells Homer he's the safety inspector, the donut and paper cup have disappeared from his hands. (00:10:05)
Tree House of Horror XII - S13-E1
Continuity mistake: In 'House of Whacks,' Homer swings an axe at the water softener, making three large dents. The shot changes and one of the dents near the bottom vanishes. (00:13:30)
Continuity mistake: When the family are driving home from the cinema, Bart draws an angry face on the back of Homer's head. It is never there at any other point in that night.
Other mistake: When Homer is crossing the rickety bridge in the snow plow there is no snow on the planks even though he is in a blizzard and the storm couldn't have just started because the path he just came from was covered in snow. (00:18:55)
Continuity mistake: At the beginning, if you watch the clock as Homer walks in, the time changes between shots. (00:01:30)
Tree House of Horror V - S6-E6
Continuity mistake: At the end of 'The Shining, ' the family sits in the snow, Homer holding Willie's portable TV. Later, when they're frozen, Homer is holding nothing, although the TV's snow-topped antenna is still there. Additionally, Homer's left shoulder is missing. This is all due to the lack of correct colorization.
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