Continuity mistake: When all the dads are together in front of Homer's house, one of them is wearing a grey sweater. When they enter the RV the man with the grey sweater doesn't, but throughout the episode he keeps appearing and disappearing on the RV.
Continuity mistake: When the Shelbyville kids drop the basket of lemons when Bart and friends start throwing lemons at them, the position of the basket changes when the Shelbyville kids run off. Note the colour of the Springfield grass and the Shelbyville grass.
Who Shot Mr. Burns? (1) - S6-E25
Other mistake: In the very first scene, when Principal Skinner is opening the door to the school, there is no name on the school. (00:00:25)
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: Homer crashes through the security barrier then skids to a halt on concrete. But, a shot later, the car is on a field which wasn't there before.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: Principal Skinner picks up the hamster and throws it away. But his hands are clean as a whistle even though all the hamster was covered with oil.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: In this episode, Mr Burns and Smithers are on the balcony of Burns' office. Mr Burns says "It will be like taking candy from a baby. Hey, that sounds like a laugh. Let's try it right now." We see Smithers, whose expression doesn't change as the two go back into Burn's office. In 'Who Shot Mr Burns Part 2', Smithers remembers this event, except now he looks quite shocked when Burns mentions about taking the candy.
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.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: When Smithers and Mr Burns are eating the chocolate and see the photo, you can see that Marge's necklace changes from red to white and then back to red.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: When Burns is pretending to be a student in Skinner's office, the door changes from open to closed and from dark blue/green to grey.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: Early on in this episode, Mr Burns says something like "this positivly has to be there overnight", the shot goes closer on every word or so. You can see that the background behind Mr Burns is that of the Plant. But when the shot zooms out, the background is now of one of the corridors.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: When Mr. Burns is sitting on Principal Skinner's desk, he takes his cap off and places in on the desk next to him. But in the next shot when Skinner is saying his monopoly is terrible, the cap is gone.
Who Shot Mr. Burns? (1) - S6-E25
Continuity mistake: When Mr. Burns falls onto the sundial, everybody starts gathering around. Marge is there, with Maggie. She left Maggie in the car and seeing as she went off to look for Homer, Bart, Lisa and Grandpa and that she was one of the first on the scene when Mr. Burns collaspses, it would be difficult to run back and get Maggie from the car.
Who Shot Mr. Burns? (1) - S6-E25
Revealing mistake: Right at the beginning, watch as Principle Skinner enters the classroom, there's a clock on the top left hand of the screen. The majority of the left side of the clock is not drawn in.
Who Shot Mr. Burns? (2) - S7-E1
Other mistake: As Chief Wiggum is being interviewed about the fugitive, his arm is shown to be in a cast due to the police van crashing at the Krusty Burger Drive-Thru earlier on. Yet when they get to the hospital, his arm is completely fine. (00:17:30 - 00:19:00)
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.
Who Shot Mr. Burns? (2) - S7-E1
Character mistake: Willie says he got arthritis from playing Space Invaders in 1977. However, Space Invaders didn't come out until 1978.
Who Shot Mr. Burns? (2) - S7-E1
Factual error: Chief Wiggum visually compares a bullet taken from Homer's gun to the bullet removed from Burns and concludes that they are exactly the same. Excluding the obvious forensic violation, the bullet removed from Burns is still whole and within its casing, meaning that either Maggie took the time to remove the casing and delicately shove it in Mr Burns' bullet wound (which is dumb) or the gun fired the whole casing along with the bullet (which would have blown up the gun).
Plot hole: The director of Radioactive Man says to Bart "we found our new Fall Out Boy. That's what I would say if you weren't an inch too short. NEXT!" But Milhouse is the new Fall Out Boy, and he's blatantly smaller than Bart. Bart was standing right next to Milhouse, so the director could see the difference.
Audio problem: After being hit with the nuclear waste, Ranier Wolfcastle says "My eyes! The goggles do nothing" without moving his mouth.
Home Sweet Home-Dum-Diddly Doodly - S7-E3
Continuity mistake: At the Flanders' house, in the kitchen, Bart and Lisa have sandwiches on plates in front of them. The shot changes and everyone on the table has an empty bowl including Bart and Lisa.
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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