Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: When all the kids are watching TV, we see Wendell, Martin and Milhouse. Absurdly they appear to be right below the ceiling in this shot - when in every other shot they are sitting on the sofa or standing.
Continuity mistake: Just before Bart's flashback, his shirt is orange, and the chair he's sitting on is blue. But in this episode, his shirt is a paler shade of orange and the chairs in the classroom are red.
Blood Feud - S2-E22
Audio problem: When Homer is kicking the postbox, Barney says something like "Fight the power" but his mouth never moves.
Oh, Brother, Where Are Thou? - S2-E15
Continuity mistake: When Herb, Bart and Lisa are watching Itchy and Scratchy, Herb goes from wearing a t-shirt and shorts to a shirt and tie between shots.
Other mistake: After the boxing match, the boys start "boo-ing" to the TV, and for a few frames Lewis goes from black to yellow, then to black, causing a flashing effect. (00:02:45)
Continuity mistake: The guardrail at the Springfield Gorge keeps changing between shots when Bart is about to make his big jump; in the first wide shot there is a short rail opposite the "stone ramp." Then in the Bart-POV shot from atop the ramp, the rail is much longer, and the parking lot and picnic area behind it have disappeared. And when Homer is actually jumping the gorge, the rail disappears altogether.
Continuity mistake: Abe's girlfriend dies in the middle of this episode, but at the end, seconds before the end credits, you can see her walk behind some other old people.
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: In every other episode, the bar at Moe's Tavern is a regular L-shape. In this episode, it has somehow gained two additional angles on the long side, making it a Z-shape (plus the angle to the short end, which is not shown).
Continuity mistake: In the scene where Lionel Hutz hands over the $106 check, Abe Simpson's room number is 18. After Abe called Homer, the manager of the Retirement Castle comes in. The number 18 has now disappeared.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: After the safety expedition has taken place, we see that when everyone is in Burns' office that by his main doors there are 4 buttons on the wall. Yet when a shot from further away is shown, they are not there.
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: After the aliens have dropped off the Simpsons in their back yard, Marge is seen wearing her usual red pearls. Except in the final shot of the family. Then her pearls are white. This is not due to the alien light source altering the colors in the segment, because Marge's pearls have been a dark color through the whole episode, even inside the alien spaceship.
Bart Gets Hit By a Car - S2-E10
Revealing mistake: After Marge has been in court, Mr Burns' lawyer says "Thank you very much Mrs Simpson", and when he does it, the top of his head above his glasses is less pale than the rest of his face.
The War of the Simpsons - S2-E20
Continuity mistake: When Homer has caught General Sherman he beats it with an oar so that the oar snaps in two. Then suddenly Homer rows with both oars intact.
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: At Sunday school, Milhouse's jumper changes from black to red between shots.
Continuity mistake: During the tournament, Abe Lincoln hole, there is only one hole to shoot for when his legs open up, after Todd hits his ball through, you see 3 holes from the backside. After Bart hits his ball the legs open up to reveal 3 holes to shoot for from the frontside. (00:19:25)
Continuity mistake: When the family is talking at the dinner table about going to see Truckasaurus, the amount of food on everyone's plate continually changes between shots. (00:03:40 - 00:04:25)
Continuity mistake: When at the dinner table, Marge tells Homer and Bart that they can go to see Truck-o-saurus. In one shot Bart has his hands on the dinner table, but in the next shot his arms are by his side. (00:04:20)
Continuity mistake: When Mr. Burns and Smithers go to leave, the beak-like knocker has disappeared from the Simpsons' front door.
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: In "Hungry Are The Damned", when the family are looking up at the UFO and Homer says that the burgers are getting cold, the burger he is eating has a bite out of it. In his close-up it is a whole burger.
Bart Gets Hit By a Car - S2-E10
Continuity mistake: In Moe's Tavern, in the close-up of Marge as she says "Homer, look at me" the glass window behind her has a different pattern than in all the other shots (2 rows of red tiles instead of 3).
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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