Continuity mistake: When Krusty ends up at his old neighbourhood, the street changes between shots. E.g. the "LLBeanie" sign appears above the door of the 2nd shop and the suit of the man reading the newspaper changes from grey to blue. (00:05:25)
Lisa's Pony - S3-E8
Continuity mistake: When Homer is phoned by Lisa, the color of the phone is blue. Immediately after, it turns to green. (00:19:00)
Continuity mistake: When Homer enters Moe's tavern, Moe is playing solitaire. The cards on the table are face down/face up between shots. (00:04:45)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When Bart and Lisa argue over which wish to make, the hand on the table changes position, and the thumb switches sides. (00:03:30)
Continuity mistake: When Mr Burns opens the note from the rocket he places the rubber band on his desk. In a following shot the rubber band changes position.
Continuity mistake: In the scene at the abandoned Penitentiary the puddle which Ralph and Bart fall into just appears from nowhere.
Continuity mistake: At the birthday party Maggie is playing in the sandbox with one of Apu's kids. She and Apu's son both have pink with green polka-dots party hats on. After she is taken out of the sandbox by Moe, Homer takes her and she keeps squirming out of his arms. Look on her head and you'll see that her party hat has disappeared, and never comes back.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: During The Town meeting scene, the position of Latin jazz great Tito Puente hops all over the room - he is frequently appearing in the background, but from various angles.
Sweet Seymour Skinner's Baadasssss Song - S5-E19
Continuity mistake: Near the beginning of the episode, Bart is thinking what it would be like to get out of school, you can see his desk quite well and there is nothing on it. But when Bart has finished thinking, a piece of paper has just appeared on his desk.
Continuity mistake: At the very end of the episode, when the kids are lined up to wait to see whether Otto is back driving the bus, there are several shots that switch back and forth between a direct view of the kids and a shot from behind. Lisa changes position between shots. (00:21:15)
Continuity mistake: After he takes a puppy from Bart, Snake's car appears from nowhere. (00:04:15)
Continuity mistake: When the family is having dinner, the glasses on the table keep disappearing/reappearing between shots. (00:09:30 - 00:10:30)
Continuity mistake: When Lisa shows her exam to her family, the "a" note keeps changing from being circled in red and in a red round. (00:04:30)
Revealing mistake: When Marge says, "Slow and steady wins the race", her face and body are two different colors.
Springfield Connection - S6-E23
Continuity mistake: When Marge sees Homer's car parked illegally over 3 handicapped spots you can see a car parked near Homer's that is orange. Later in the scene when Marge starts writing a ticket up for Homer the car next to Homer's is now a dark brown. (00:14:35 - 00:15:05)
Plot hole: In the car chase, Chief Wiggum says that one of the suspects (Marge) "is wearing a green dress, pearls, and a lot of blue hair." However when we see Marge from the police car all we can see is her hair, so how would he have known about the pearls and dress?
Revealing mistake: When Lisa is clapping erasers, you can see the alphabet above the board, and part of the A is cut off.
Continuity mistake: When Homer stands on the nail in the back yard, you can see behind him, that on the wall next to the back door there are two purple lights. Seconds later when Lisa shows him the new doghouse, the lights have gone. (00:17:25)
Tree House of Horror V - S6-E6
Continuity mistake: In 'Nightmare Cafeteria,' in the opening shot we see Bart standing on a desk in the back row. It cuts to a closeup, and he is now on a desk in the second row from the back, as well as people appearing around him, such as Milhouse, who wasn't even in the classroom in the opening shot. (00:15:25)
Tree House of Horror V - S6-E6
Continuity mistake: In 'Nightmare Cafeteria,' when Lunchlady Doris spills food on Jimbo, it only goes onto him. In the next shot it is also all over the table. (00:16:15)
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