Continuity mistake: Rodd's hair is black when him and Todd are in bed singing. It can't be because it's dark, because Todd's hair is unchanged. (00:15:10)
Moaning Lisa - S1-E6
Continuity mistake: When Marge is driving Lisa to school, in one shot you can see that her necklace is red. Then in the next shot it is white. It then changes back to red and stays that way.
Bart Carny - S9-E12
Continuity mistake: At dinner when the carny dad is doing his cigarette trick, the shot changes to Bart and Lisa and they have piles of food on their plates. About 10 seconds later Marge gathers the plates up and there is nothing on them. Are we to believe that they ate all this food in such a short space of time?
Continuity mistake: Bart's guitar is lefthanded. So when the righthanded Otto plays it on the bus, the guitar is flipped over, with the little speaker on the top. But when Otto is playing it later in the garage, it is a normal righthanded guitar, with the little speaker on the bottom.
Continuity mistake: When Homer is at the retirement party, there is a far shot of him (when Smithers talks to Mr. Burns) and he isn't wearing his jacket. In every other shot Homer is wearing his jacket. (00:05:20)
Continuity mistake: In Moe's, Homer points at Lenny and says "Are you calling me a liar," with the same hand which is instantly holding a beer in the next shot.
Lisa on Ice - S6-E8
Revealing mistake: After the buzzer goes on the final game and the crowd reacts one of the crowd members says "Tie Game.", then some woman in a red top says "What the Hell.". If you look at the woman when she moves her head you can see the nose on her face disappears. (00:19:55)
Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Lisa meets Clara, there is a close up of her necklace. The necklace is never there in any of the other shots that we see her. Her ring, as also seen in the close-up isn't visible either.
Like Father, Like Klown - S3-E6
Continuity mistake: When Miss Pennycandy barges in on Krusty's 'Sex Chat,' she leaves the door open. It remains closed for the rest of the scene. (00:04:15)
Continuity mistake: When Homer hands over the key to Mayor Quimbey, the mayor points out the teeth marks on it. But in the next shot when Homer says he thought there was chocolate inside, the bite marks are gone. (00:16:30)
Continuity mistake: When Homer buys Ned's living room for $75, Bart is wearing a pink "Ned loves Maude" T-Shirt but by the end of the scene where Bart says "Hands off my china hutch." his shirt is the standard orange shirt. (00:14:40)
Continuity mistake: In the park, Marge's necklace changes from white to red. (00:15:40)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: In the scene where Marge is talking to Bart's teacher, Marge is "punished" by writing lines on the blackboard. In the first shot of her doing so she has written the line 9 times, but in the next shot there are 11 lines. (00:05:10)
Homer vs. Lisa and the 8th Commandment - S2-E13
Revealing mistake: When Homer is imagining being locked in the jail cell and he turns around to find he is in his own home, he turns to look at his family. There is a close up shot of his terrified face, and the people in the background watching the game (I think it might be Lenny and Carl) have no eyes. The rest of their face is fine, but their eyes are missing.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing And I", Bart discovers he has a scar where he was separated from Hugo. During the attic scene, it disappears. (00:04:40 - 00:06:10)
Continuity mistake: When Homer is making a note for Marge, he scribbles out Patty's name and writes his own. When he writes it, the "signature" is neat, but when Marge reads it, it's sloppy. (00:14:30)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: After Lisa declares world peace, when the two UN guys hug each other, the United Nations symbol on the wall has changed from purple to blue. (00:05:25)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: When Homer picks up the monkey's paw for the first time, a person walks behind him. He has disappeared in the next shot. (00:02:35)
Continuity mistake: When Homer is gambling with the gangsters, you can just barely see the shoulder of an ORANGE shirt that Bart is wearing, but in all other shots he is wearing his tuxedo. (00:12:10)
Continuity mistake: When Homer says, "You can't take our donuts," his hat is red. But in the next shot and in every other shot of Homer, his hat is blue. This is pointed out on the audio commentary on the Season 4 DVD. (00:12:35)
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