Continuity mistake: In the bit where they sit on the sofa at the start of each episode, there is one rather long one where it starts off with the Simpsons dancing in a line, then gradually evolves into a circus with elephants and men dancing around fire. Look closely in between Homer's right leg and the dancing woman on his right. There is a pile of books on the little shelf underneath the lamp and telephone, and just as the camera starts zooming out from the line of dancing, the orange book on the left noticeably changes to purple. (00:01:20)
Continuity mistake: When Marge and Homer are arguing about Don Quixote, Marge's pillow disappears from under her head. (00:09:50)
Continuity mistake: While Homer is sleeping, the fire burns off the hair on his head. But when he wakes up and jumps up off the couch, his hair is back again. (00:17:00)
Kamp Krusty - S4-E1
Factual error: In the last scene, with the picture of the bus leaving Tijuana, it says "Leaving Tijuana" above the gate leading into the city.
Continuity mistake: When Krusty the Clown arrives at the beauty pageant his tie is done up. When he goes on stage it is undone.
Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Continuity mistake: When Homer is escorting his family out of the house to escape the Zombies, he leaves the door wide open, but in the very next shot it is shut. (00:18:50)
Revealing mistake: At the car convention, Homer chides Bart through the windscreen of Bonnie and Clyde's car. However, Homer's body is not seen through the holes in the windshield, which shows that the holes in the windshield were achieved via a layer of red-coloured holes. (00:04:25)
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)
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: 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)
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)
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)
Kamp Krusty - S4-E1
Continuity mistake: In the shot where Kearney is reading the letter sent by Marge whilst he is eating the jellybean cookies, there is a quick shot of Kearney's hand going to his mouth with the cookie to eat it. Note that there is nothing on his wrist. In the next shot where it is revealed that Kearney is reading the letter rather than Bart or Lisa, he has spiky, black collars on his wrist. (00:14:25)
Kamp Krusty - S4-E1
Continuity mistake: When the kids rip Krusty's shirt to see if it is the real him he buttons his shirt up then in the next shot his shirt is still torn.
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When there is a queue to see the movie, it stretches right back to the Simpson house, and we see Bart looking through the window. However, when Homer talks to Bart whilst sitting on the window, the queue has disappeared. (00:16:45)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Bart and Lisa are watching TV, Bart says something like 'I've got my ticket' and pats a ticket that is inside his shirt pocket (which there is none). But later in that same scene when they are still watching TV, both the pocket and the ticket have gone. (00:12:20 - 00:14:15)
Continuity mistake: The old men beside Grandpa when Homer plows the retirement home switch places, depending on whether it's a long or a close shot. (00:10:00)
Itchy and Scratchy: The Movie - S4-E6
Continuity mistake: When Maggie is driving Homer's car, a man is behind him. He is seen waving his left arm but when the shot changes to Maggie he is waving his right arm. (00:14:50)
Kamp Krusty - S4-E1
Continuity mistake: Homer points out to Marge that now that the kids are away, he has grown two more hairs, making it four on the top of his head. Later when they are reading Lisa's letter, he has two hairs again. But later still when they are watching TV, he has four again. Two of them fall out when he see that Bart is the ringleader, leaving him with his original two. (00:15:35)
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