Much Apu About Nothing - S7-E23
Continuity mistake: When Homer comes home with Apu, Lisa closes the book she's reading and slides it to the side on the sofa. When she stands in the next shot,the book has gone.
I, (Annoyed Grunt)-bot - S15-E9
Continuity mistake: The jagged piece of metal that Homer pulls from his arm disappears from the bedside table in the very next shot. (00:16:30)
Springfield Connection - S6-E23
Continuity mistake: When Marge is making celery soup, The Front view of her shows just the chopping board in front of her. Then when Lisa talks to her the microwave is seen in front of her.
Continuity mistake: When Nelson is handed the knife by his two friends, Martin, Bart and their cars have disappeared for two shots. (00:13:45)
Continuity mistake: As Nelson crosses the finish line at the time trials, The Front piece of wood on Bart's car breaks off. It is attached to the car again in the next shot. (00:14:10)
Tree House of Horror II: A Simpsons Halloween - S3-E7
Continuity mistake: At the very end of Part 1, Homer changes position between shots, and when Flanders wants a huge castle, it suddenly changes back to his normal house. (00:08:30)
Continuity mistake: In the scene where Homer decides he wants to stay with Lurlene, she locks the door about 3 times before going to kiss Homer, but when Homer leaves, he just opens the door, he doesn't unlock anything.
Continuity mistake: The "dummy" in the episode changes consistently from a real character to a dummy sometimes. When Mel jumps into the vehicle in the museum the "dummy" moves aside. When Mel shoves it out of the way, it stays in one rigid position as if it is a dummy. During the chase, the "dummy" falls on the car behind and its facial expression changes. But when one of the guys from THAT car (not the one Mel was in) goes to the dummy, its head is ripped off and you can see that it is stuffed.
Tree House of Horror XII - S13-E1
Continuity mistake: In 'Hex and the City,' as they walk through Ethnictown, Marge has a handbag over her shoulder. But in the closeup when she says "Oh, listen.", the bag has gone. (00:01:15)
Continuity mistake: When Krusty the Clown arrives at the beauty pageant his tie is done up. When he goes on stage it is undone.
Continuity mistake: When the Repo Man takes Marge's ring, we see the ring on her left hand. It wasn't visible in the shot before. (00:14:40)
Lisa's Pony - S3-E8
Continuity mistake: When Homer tells the family where the horse will be kept, if you look in the background there are drapes on the wall. These drapes weren't visible when Marge and Homer walked in the kitchen.
Continuity mistake: When Bart arrives home after his bad day, he is seen wearing his lucky red hat. It was never visible anywhere before he got home. (00:07:10)
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.
Skinner's Sense of Snow - S12-E8
Continuity mistake: When the children are sleeping in the canteen at school, Bart is resting his head on a red sweater. In the close up of him and Lisa, the sweater has now turned dark green. It's not because of the dark that we see it like that because there is a bit of light at the beginning of the next shot and we see the jumper to be dark green.
Continuity mistake: The "Stinger" only appears on the boxing gloves after Moe passes them to Homer. It is not there in all preceding shots.
Sunday, Cruddy Sunday - S10-E12
Continuity mistake: When Homer tells Lisa who is going with him to the Super Bowl, he says Comic Book Guy is going. In the shot showing the people lining up, Comic Book Guy is not there. He then appears on the bus later on.
Tree House of Horror X - S11-E4
Continuity mistake: When The Simpsons go home they find the words 'I know what You Did' on their door, written in blood. Then another shot after, you can see the door with nothing on it.
Continuity mistake: After Homer pushes in front of Lisa in the queue for the bathroom, she loses the toothbrush she was holding in her left hand. (00:01:15)
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)
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