Last Exit to Springfield - S4-E17
Continuity mistake: When Mr Burns is telling Homer to resign, he has glasses on in the first shot in the scene. However his glasses are on his desk the next shot onwards.
Homer vs. Patty and Selma - S6-E17
Other mistake: When Homer burns a dollar bill, he turns his cigar around 180 degrees. If you look carefully, the smoke soon comes from the different side than it did earlier.
Simpsons Bible Stories - S10-E18
Continuity mistake: Homer as Solomon cuts the pie into a roughly 1/3 and a 2/3 piece, but when he picks the pieces up, it's more or less halved.
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.
They Saved Lisa's Brain - S10-E22
Character mistake: The plural form of ignoramus is ignoramuses, not ignorami. The word "ignoramus," a Latin verb-form meaning "we do not know," has no Latin plural-noun form. Therefore, when used as an English noun it correctly pluralizes as "ignoramuses." Someone as smart as Lisa should know this.
White Christmas Blues - S25-E8
Continuity mistake: While Mayor Quimby is giving his speech, Moe is in two places at once. He is simultaneously standing next to Mayor Quimby and amongst the crowd of people.
Continuity mistake: When Mr. Burns is confronting Homer about his missing slave, Homer's donut is half eaten. During the next scene the donut has a smaller bite taken out of it. (00:14:00)
Character mistake: Lisa states that Pierre and Marie Curie both died of radiation poisoning. This is incorrect, as only Marie died of radiation poisoning while her husband Pierre was killed by a horse and cart. (00:08:30)
Continuity mistake: When the family are on the conveyer belt at the beginning the family are travelling along. In the next shot (the close up) they are travelling alot slower.
The Secret War of Lisa Simpson - S8-E25
Other mistake: When Lisa looks down from the platform before crossing the obstacle course, you can see her feet, but not the platform she stands on. (00:19:04)
Continuity mistake: Lenny says that Homer got his job by showing up when the nuclear plant was opened. In the episode "I Married Marge" (Season 4), the plant is already open when Homer interviews for a position, doesn't get it, then works at Gulp 'N' Blow.
Continuity mistake: When Lisa opens the classroom door (opposite the teacher's desk) and is shocked to see Miss Hoover has returned, note the door opens outward (into the hallway) and the doorknob is on the right side of the door. When Lisa runs out of the classroom, that door now opens inward and the doorknob is on the left side of the door. (00:13:40)
Continuity mistake: The card Bart has written for Milhouse is blank inside. However when Lisa looks at the card, the pun of the joke (on The Front of the card) is now there. (00:01:15)
Homer's Barbershop Quartet - S5-E1
Character mistake: When Marge is making a model of Homer for Bart and Lisa, she makes him bald with his hair round the back of his head as we all know it, but at this point in the story Homer was not yet bald. (00:18:15)
Continuity mistake: When Comic Book Guy turns off the water hydrant, the two boys in purple and blue trunks change position between shots.
Character mistake: When Bart fakes being sick, on his way to the infirmary he passes the door with a sign that reads "maintanence" but the proper spelling is "maintenance", and when Bart reaches the infirmary, the sign on the door reads "ineirmary." (00:07:30)
Bart Carny - S9-E12
Continuity mistake: When the Simpsons drive up to the house, there are no boards on the window. When they can't get in, suddenly there are boards on the windows.
Treehouse of Horror XV - S16-E1
Continuity mistake: When Maggie crawls out of the stroller and into the capsule, the stroller has no harness, but when Marge sees the empty stroller, there is a harness.
Who Shot Mr. Burns? (2) - S7-E1
Factual error: When Chief Wiggum opens the revolver's chamber, there's 5 rounds with one open slot. In the next shot, we see the reverse end of the chamber and it's drawn in such a way to indicate those 5 rounds all have bullets in them still, meaning the empty slot is from when Maggie shot Mr. Burns. But revolvers don't eject spent shells automatically and no one handled the gun after it dropped on the floor. So the empty casing should have still been in there when Wiggum opens it up for the first time.
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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