Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: Homer asks Bart if he took the bins out. When Homer walks into the kitchen, the time on clock changes. (00:10:00)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: What the goats are eating changes depending on the shots. (00:10:10)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Bart and Lisa are watching TV, Bart says something like 'I've got my ticket' and pats a ticket that is inside his shirt pocket (which there is none). But later in that same scene when they are still watching TV, both the pocket and the ticket have gone. (00:12:20 - 00:14:15)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Maggie is driving Homer's car, a man is behind him. He is seen waving his left arm but when the shot changes to Maggie he is waving his right arm. (00:14:50)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Homer is about to punish Bart, his ticket suddenly appears in a shirt pocket. (00:15:10)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: Homer rips up Bart's ticket and the bits land on the floor. Only to simply vanish into thin air. (00:15:20)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When there is a queue to see the movie, it stretches right back to the Simpson house, and we see Bart looking through the window. However, when Homer talks to Bart whilst sitting on the window, the queue has disappeared. (00:16:45)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Bart places his money on the kiosk, the end of the note is overhanging the edge of the kiosk. When he grabs his money after being refused entry, the entire note is on the kiosk. (00:19:20)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Bart tries to buy a ticket to Itchy and Scratchy, the booth is unoccupied. When the shot changes the man has appeared in the booth. (00:19:20)
Continuity mistake: We see the items fall off the roof but a Christmas ornament is not among them. However one lands on the ground with everything else. (00:02:05)
Continuity mistake: When stuff is falling off the roof, in the long shot there is nothing on the roof but in the close up there is. (00:02:05)
Continuity mistake: When Homer is at the retirement party, there is a far shot of him (when Smithers talks to Mr. Burns) and he isn't wearing his jacket. In every other shot Homer is wearing his jacket. (00:05:20)
Continuity mistake: During the musical number about Mr. Burns, Homer and Marge swap sides of the table. (00:05:40)
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 the family is at dinner, there is a top down view which zooms in on them from above. In this shot there is no newspaper on the chest (to Homer's left). In the next shot of Homer a newspaper has appeared. (00:07:50)
Continuity mistake: When Homer is talking about Marge getting a job at the dinner table he has a spoon in his hand. Once Marge has finished scowling he doesn't, and there isn't one on the plate either. (00:08:05)
Continuity mistake: Mr. Burns gives Marge a present when she starts her new job. The present is light purple with a red ribbon around it. Seconds later though, the present turns to orange with a red ribbon around it. (00:11:45)
Continuity mistake: When Homer says, "You can't take our donuts," his hat is red. But in the next shot and in every other shot of Homer, his hat is blue. This is pointed out on the audio commentary on the Season 4 DVD. (00:12:35)
Continuity mistake: When Burns is lay on the floor telling Smithers that he dreamed of Marge again last night, the painting behind Smithers is very badly painted and very childish in appearance. Burns' head is completely disproportionate for example. When the shot changes to Smithers the painting is now a lot more detailed and no longer looks childish. (00:14:42)
Continuity mistake: When we see Smither daydreaming about Mr Burns coming in through his window at night, the painting on the wall disappears between shots. (00:14:50)
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