Continuity mistake: When Bart falls off his skateboard after attempting to skate over Homer's car, as the shot zooms out you can see his board is nowhere to be seen. (00:11:05)
Continuity mistake: As Milhouse walks up to the TV to turn up the volume, Lewis is nowhere to be seen in a wide shot, but as Milhouse walks back over to the couch you can see Lewis sitting on the floor. (00:02:15)
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.
Continuity mistake: When Flanders' wife gives them the sandwiches in the recreation room there are 12 sandwiches, when Homer asks Ned to get him a beer there are only 6.
Continuity mistake: When Homer falls down the gorge, the medics lift him up on a bungee and to the top of the cliff. Between shots the edge of the cliff changes from green grass to brown rock. (00:20:05)
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: When Homer is sitting watching cable, the rest of the family comes home and one of them is carrying a plant in a pot, which is put down next to the couch. While they watch and watch cable, it grows very tall and then withers down. When Homer goes behind the TV and starts kissing the wires, the plant has moved to next to the doorway and is suddenly fully grown again.
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)
Continuity mistake: When Lisa shows her exam to her family, the "a" note keeps changing from being circled in red and in a red round. (00:04:30)
Continuity mistake: In the scene where Bart and Homer find Marge's paintings in the attic, there is a shot of the paintings all stacked up and you can see that the edges of all of them are the same shade of pink as The Front painting. However, when the boys flick through the paintings, the backgrounds and edges are a variety of colours, including pale blue.
Continuity mistake: When Patty and Selma bring food to the Simpsons' for one shot Patty's dress turns blue before turning purple again.
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: When the family are outside, in the shot just after Homer says "At the worst possible time" you can see the living room - everybody has disappeared in that shot.
Continuity mistake: When Homer is driving to Truckasaurus there is a wide shot of the road with two cars on it, but in the next side shot of the road, the road has loads more cars on it. (00:06:30)
Bart Gets Hit By a Car - S2-E10
Continuity mistake: During Marge's testimony, Lionel Hutz has a neat stack of papers in front of him the whole time. But in the close-up when Homer and Hutz both cover their eyes in sorrow, Hutz has several pieces of crumbled paper and a broken pencil in front of him. The was not nearly enough time for him to make such a mess since the last shot of him.
Continuity mistake: When Bart attempts to skate over Homer's car, his three mates are watching. Between shots they change from standing on the driveway to standing on the pavement. (00:10:55)
Three Men and a Comic Book - S2-E21
Continuity mistake: When there is a rotating shot of Bart, Martin and Milhouse up in the treehouse, the shot never goes past the table, even though it should.
Homer vs. Lisa and the 8th Commandment - S2-E13
Continuity mistake: When the door is answered to Mr Burns and Mr Smithers, Barney is seen answering, who has orange sleeves. However when the door is opened, you can just make out a white sleeve, which could be none other than Homer's.
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)
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.
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