The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When Bart is unpacking his things from the box, if you look at the mantelpiece, we can see that there is a candle on the right hand side of it. But later on, there is a candle on the left hand side which wasn't previously there. (00:02:30 - 00:03:15)
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: In Hungry are the Damned, when The Simpsons are on the spaceship and the aliens show them the food, there are 3 pots and two plates. Yet when the shot changes there are 4 pots and no plates. (00:10:25)
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When the Simpsons are about to eat on the spaceship, in one shot just before they eat there are 3 candles on the table, and when they all sit down they're gone. (00:10:40)
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When Homer is preparing the barbecue, he is wearing an apron that says "Mafia staff apron". After he goes to pick up the lighter fluid, it reads "Maffia staff apron", and after he has lit the barbecue, it is back to saying "Mafia".
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.
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.
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When the Simpsons are eating for the second time the alien on the very left, which previously had spots on his cheek, now has no spots.
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: In the Raven scene, you can see Homer's drool on his jacket, but in the next shot and following shots it's gone.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: The shot glass that Burns places on his desk disappears for several frames before reappearing. (00:05:45)
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.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Marge is standing outside the Kwik-E-Mart, she is holding some papers with a picture of Mary Bailey and the words "Re-Elect Bailey." But in a long shot of Marge in the next shot, the papers she is holding in her right arm are now completely blank.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mr. Burns is drinking on his desk, a frame is misplaced. His shot glass, for a split-second, moves from its original position, to the edge of the table, and back.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mr Burns tells Homer to wreck something, Homer throws a plant pot onto the floor and it breaks into several pieces. When Mr Burns tells Smithers to take him home, the pieces of the broken plant pot are nowhere to be seen.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Marge carries the plate with a cover on to Mr Burns, you can see there is nothing by Bart on the corner of the table, but in the next shot a plate suddenly appears.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: During the dinner scene towards the end of the episode, Mr Burns puts his knife on top of the knife and spoon. Later on, the items of cutlery are now lying in a row.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When the family are having dinner with Mr Burns, you can see that Bart and Mr Burns have by their plates a fork, a knife and a spoon. In the next shot, the knife and spoon disappear.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When the cat comes out of the Simpsons' house, the doormat is blue. When Mr Burns goes into the house, the doormat is green.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Mr Burns knocks on the door of the Simpsons' house, there is nothing on the door, but in the next shot, a door knocker appears.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Homer knocks Marge off the bed, there is a small purple object by the lampshade. When she is back in bed, the object has gone.
Two Cars in Every Garage and Three Eyes on Every Fish - S2-E4
Continuity mistake: When Marge tells Homer that she's going to ringing doorbells for Mary Bailey, Homer says "Doh!" and there is nothing beside him on the table. In the next shot, a bowl and a cup have appeared.
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.
Xofer