Tree House of Horror V - S6-E6
Continuity mistake: In 'Time and Punishment,' when the machine picks up the Simpsons' house, to take it to the 'Re-Neducation Centre,' the garage is on the wrong side of the house. It is on the correct side in the following shots of Homer returning. (00:11:20)
Continuity mistake: When Lisa knocks Bart's chop out his mouth she knocks it out front, however, the chop ends up going to the far right and into Homer's mouth.
Continuity mistake: When Krusty is sacked, his bottle of pop vanishes. (00:13:45)
Continuity mistake: At the end of the episode when Marge is first seen doing the entertainment, the shot shows (from left to right): Flanders, Skinner, Kirk Van Houten, Kent Brockman, Mayor Quimby, Grandpa, and behind them, Lionel Hutz, Lenny, Homer and Dr Hibbert. In a following shot from behind Marge the guests have changed places. Reverend Lovejoy is on the end, then Flanders, then Skinner, then Mr Burns, then Grandpa. There is a seat next to Grandpa which is blocked by Marge's head. Also Lionel Hutz has moved far back. Where did Burns appear from and where did Kirk, Mayor Quimby, and Kent Brockman all go?
The Call of the Simpsons - S1-E7
Continuity mistake: When the cameraman is filming Homer in the mud, he screams quite a few times. Yet on the news report showing the footage, we only hear Homer yelling and not the screams. (00:16:00)
Continuity mistake: In the cafeteria at the power plant, in the wide shot the clock on the wall is on 9.00, but closer up it's showing 10.35.
Sideshow Bob's Last Gleaming - S7-E9
Continuity mistake: When Maggie (sitting on Marge) appears on "Tyrano-Vision," Homer waves his hand in front of her. However, we can see that he isn't leaning over too far, and in the next shot it is clear that both Bart and Lisa are sitting between Homer and Marge, so there is no way he could have reached over to her in the first place.
Much Apu About Nothing - S7-E23
Continuity mistake: When they are locating 'Springfield' on the map the coffee jug on the table is about 1/4 full.In the last shot of Apu the coffee has risen to about 3/4 full.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob leave Quimby's office, he had loads of things on his desk. When he pulls the picnic basket up, the desk is empty.
The Springfield Files - S8-E10
Continuity mistake: After the scene with the T-shirts, when the alien arives, Marge's "Homer is a dope" shirt disappears and she has her normal dress on.
Continuity mistake: At the end in the hospital, Maggie's bow is red for a second, then it changes to blue.
Thirty Minutes Over Tokyo - S10-E23
Continuity mistake: Marge loses one of her shoes in the "lava" , but when they fall down, Marge wears two shoes again.
Continuity mistake: When Bart falls down the stairs, you see him fall down at least 50 stairs in the close up. There are never this many on the full shots of the staircase.
Continuity mistake: When Homer and Barney are talking about the lottery, Barney says, "130 million." Then, they set their mugs on the table but when they all run off their mugs have disappeared. (00:01:50)
It's a Mad, Mad, Mad, Mad Marge - S11-E21
Continuity mistake: When Otto meets Becky at 'Der Crazy Kraut', there are a lot of children in the bus windows. However, just before he gives her the ring, the kids have now vanished.
The Boy Who Knew Too Much - S5-E20
Continuity mistake: Hans Moleman's clothes change from white to black during the trial. (00:12:05 - 00:13:25)
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.
Last Exit to Springfield - S4-E17
Continuity mistake: When we see McBain at the beginning of the episode, after shooting some people, the magazine falls out of the machine gun. But from the next shot onwards it is back in the gun.
Continuity mistake: When Burns first shows the team the nerve tonic, the "&" on the 'Brain & Nerve Tonic' label is facing backward, but as Burns pulls it away it faces forward. Then as he moves it around as he's talking, the "&" switches between facing forward and facing backward again. This happens all in the one shot.
Continuity mistake: The shaving cream on Chief Wiggum's face disappears when Bart tries to confess about the phony kidnapping.
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