Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Continuity mistake: When Homer is escorting his family out of the house to escape the Zombies, he leaves the door wide open, but in the very next shot it is shut. (00:18:50)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Homer is in Lisa's classroom and imitates a farting sound, there is a sink at the back of the classroom and nobody is using it. However in the wide shot, there are suddenly two people by the sink. When the shot is back to Homer, nobody is by it. (00:03:00)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: In the scene where Marge is talking to Bart's teacher, Marge is "punished" by writing lines on the blackboard. In the first shot of her doing so she has written the line 9 times, but in the next shot there are 11 lines. (00:05:10)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Bart is looking for food in his bedroom, he throws a book towards Santa's Little Helper. The position of this book and it's pages changes between consecutive shots. (00:08:20)
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)
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.
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