Lisa's Pony - S3-E8
Continuity mistake: The number of knives that Sherri is holding changes between long and close shots at the talent show. (00:04:50)
When You Dish Upon a Star - S10-E5
Trivia: Another thing "The Simpsons" predicted: Towards the end of this episode, a sign outside of a film studio shows the 20th Century Fox logo with "A Division of Walt Disney Co" written under it. Nineteen years after this episode aired, Disney purchased many assets from 20th/21st Century Fox, including "The Simpsons."
Cape Feare - S5-E2
Continuity mistake: When the Simpsons get out of the car at Terror Lake, there are no rakes on the ground. When Bob gets out of the car, there is a whole stack of them. (00:14:30)
Continuity mistake: When Homer is in Moe's, Moe pours him a full pint. When it's passed to Homer, it's now 3/4 full in the glass. (00:10:40)
Continuity mistake: At the start, Homer has his feet on the floor until Ruth asks for a sander, and one suddenly appears under Homer's feet. (00:02:30)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, just as Millhouse is getting ready to move seats, he's sat with his hands in his lap until the shot changes, and then he is holding a red book. (00:12:00)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, as Bart is being stretchered away, he is sat up on the stretcher, but when Skinner says, "perhaps a life at the mad house..." Bart is now lay down. (00:14:05)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, Bart has a nightmare and walks into the kitchen, and there is no bowl in front of him. When Lisa speaks, a bowl appears in front of Bart. (00:09:10)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, Bart throws his spoon when Homer blasts the air horn. When the shot changes, the spoon has reappeared in the bowl. (00:09:30)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, when Bart gets scared by Homer, there is a spare bowl on the table right next to his. When the shot changes, this spare bowl has disappeared. (00:09:30)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: In Terror at 5 1/2 Feet, the size of the notepad above the phone changes several times. (00:09:30)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: When Homer finishes his donut, the number of bits of paper on the fridge changes from 3 to 4. (00:03:20)
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Continuity mistake: When Homer is being taken to hell, his position in the floor keeps changing. Note the tile patterns. (00:03:40)
Homer's Barbershop Quartet - S5-E1
Continuity mistake: The wording "Be Sharps" changes size on the album when the family is laughing at Bart. It gets much smaller. (00:04:00)
Homer's Barbershop Quartet - S5-E1
Continuity mistake: When Bart and Lisa find the record Melvin and the Squirrels, they hand it to the Comic Book Guy to play. While the record is in his hand you can still see it displayed on the rack. (00:03:40)
Homer's Barbershop Quartet - S5-E1
Continuity mistake: Skinner puts the helmet on his head and we see Hermann from inside the helmet, and he has no cigarette in his mouth. When we see the shot from outside, he does. (00:03:10)
The Fat and the Furriest - S15-E5
Continuity mistake: When Homer and the bear face each other in the cave, he's barefoot, but when he removes the electric prod from the bear's ear, he inexplicably wears shoes, and then he's barefoot again when he puts it on his ear.
Continuity mistake: When Bart runs his nails down the chalkboard, the image on the board changes slightly; note the legs. There is a gap between one leg and the body in one shot, but not the other. (00:14:00)
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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