Continuity mistake: After the boy's car gets crushed, Bart sells Milhouse's glasses for $600. Then Milhouse knocks over the Coke bottles and the clerk gets the money back and keeps the glasses. The next scene, where they try to get on a train that goes to Springfield, you can see Milhouse in his glasses and throughout the rest of the episode.
22 Short Films About Springfield - S7-E21
Continuity mistake: When Skinner and the superintendant are having lunch, Skinner brings in four burgers. The superintendant takes one, and suddenly there is only one left.
22 Short Films About Springfield - S7-E21
Other mistake: When Chalmers and Skinner are having lunch with hamburgers, Chalmers bites it. When he opens it, the bread's slice is bitten but the meat is not.
22 Short Films About Springfield - S7-E21
Continuity mistake: Lisa comes out of the hairdresser's with a new hairstyle which Nelson laughs at. She is walking away to Nelson's right yet when Nelson's being chased by a tall man later and flees around a corner to his left she's suddenly standing there.
22 Short Films About Springfield - S7-E21
Revealing mistake: A black line briefly appears on Apu's forehead while he's tossing the tofu dog around.
Raging Abe Simpson and His Grumbling Grandson in 'The Curse of the Flying Hellfish' - S7-E22
Continuity mistake: At Asa's funeral Burns and Grandpa both produce a key to unlock the compartment in the Hellfish monument, but even though they both take their keys out of the keyholes after turning them, all 9 keys are in place in the following shots.
Raging Abe Simpson and His Grumbling Grandson in 'The Curse of the Flying Hellfish' - S7-E22
Continuity mistake: Grampa loses his red slipper as he is pulled by Mr. Burns' boat. Later it is back on his foot.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob come to Quimby's office for the first time, the items on his desk change colour and position.
Much Apu About Nothing - S7-E23
Plot hole: At the end Apu finds out he's been chosen for jury duty for the first time. However, in 'The Boy Who Knew Too Much' he was on the jury.
Much Apu About Nothing - S7-E23
Continuity mistake: Willy jumps in and shakes his fists at the children and Skinner who are in a circle around him. Uta has now disappeared from the circle and cannot be seen anywhere when he was there just seconds before.
Much Apu About Nothing - S7-E23
Continuity mistake: When Kearney buys the beer, the shot of the ice cream sandwiches melting in his arm pits shows that the 'Duff' writing on the crate of beer is thinner than previously seen.
Much Apu About Nothing - S7-E23
Continuity mistake: When they are locating 'Springfield' on the map the coffee jug on the table is about 1/4 full.In the last shot of Apu the coffee has risen to about 3/4 full.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob leave Quimby's office, he had loads of things on his desk. When he pulls the picnic basket up, the desk is empty.
Much Apu About Nothing - S7-E23
Continuity mistake: When Homer comes home with Apu, Lisa closes the book she's reading and slides it to the side on the sofa. When she stands in the next shot,the book has gone.
Much Apu About Nothing - S7-E23
Continuity mistake: When Homer,Barney and Moe are in Moe's making signs Moe says 'But they ain't bothered...' and leans on the pool table with his elbow.In the next shot he is leaning on it with his hand.
Much Apu About Nothing - S7-E23
Continuity mistake: When Barney is tranquilised, he falls with his mouth closed. In the following shots, it's open, closed, then open again.
Much Apu About Nothing - S7-E23
Continuity mistake: When Homer swings on the electric cable when attempting to get to his car, the cable has just appeared from nowhere because, the previous 'birds eye view' shot showed no cable.
Much Apu About Nothing - S7-E23
Continuity mistake: When Ned is struggling to get in the house at the beginning the door knob is light brown, then dark brown in another shot.
Much Apu About Nothing - S7-E23
Continuity mistake: When Apu introduces Professor Frink there are people either side of him but no Apu. In the very next shot Apu has appeared from no-where and is standing beside the Professor.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob come back to Quimby to complain about the 'Bear Tax' he opens the left door inwards.In a following shot both doors open outwards.
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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