Tree House of Horror V - S6-E6
Continuity mistake: In "The Shinning", Smithers is helping Mr Burns to put crates of beer into the car and you can see there is nothing on the lid on the car boot, but in the next shot a wheel appears from nowhere.
Continuity mistake: After Homer's emotional outburst about the lack of bananas, when it cuts to the exterior shot of the Lovejoy house the doorknob is on the right side of The Front door, but when Reverend Lovejoy kicks Bart out of his house, the doorknob is on the opposite side. Later, when Jessica twirls the baton, the doorknob is on the right side again. (00:08:00)
Continuity mistake: When Bart is talking to Jessica after she stole the collection plate money, she is far away from Bart. But when Bart says "but you're not very nice", she is right next to him.
Lisa on Ice - S6-E8
Continuity mistake: When Lisa throws her academic alert into the trash, she jumps half way across the stage without taking a step.
Lisa on Ice - S6-E8
Continuity mistake: The turtle that Homer hands to Bart disappears as soon as it goes into Barts' hand, and it is never seen again.
Homer Badman - S6-E9
Continuity mistake: When Homer's badly-edited "Rock Bottom" interview is shown on TV, the hands on the clock behind him keep jumping around between all the different cuts. But when we saw him giving the actual interview earlier, the clock behind him stayed at 5 o'clock the whole time. The hands on the clock are also slightly different.
Homer Badman - S6-E9
Continuity mistake: Homers car gets blown over by a helicopter, and gets dented, and all the windows smash. But in the next overhead shot the car is parked on the side of the road, perfectly intact.
Homer Badman - S6-E9
Continuity mistake: Just after Marge's left jacket pocket bursts open at the candy convention the shot changes to a shot of Marge's face. The next shot her right pocket has suddenly burst as well and the candy in it is no where to be seen.
Homer Badman - S6-E9
Continuity mistake: When one of the pockets of Marge's coat explodes (when Homer is stealing the rare Gummi), a huge pile of candy comes pouring out. When she bends down to pick some up, there isn't nearly as much candy there as before. There are people picking up the candy with her, but they would have to pick it up extremely fast, and they aren't.
Homer Badman - S6-E9
Continuity mistake: When Homer mixes the Pop Rox with the soda he leaves the Pop Rox packaging over the can. After he throws the can and we see it in the air the Pop Rox packaging has disappeared.
Homer Badman - S6-E9
Continuity mistake: After Marge's left pocket rips in the candy convention, she goes to start picking up the candy when we see that the right pocket has ripped all of a sudden. When Homer and Marge start running away the pockets are no longer ripped and full of candy again.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: Homer leaves the Simpson house to go to the farm house in the station wagon, and when he parks in front of the farm house he's driving his pink car.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: While hiding the fact they are looking at sex books from Bart and Lisa, Homer picks a green book. When we see what he's reading, it's a grey "Maple Thorpe" book.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: On the book on conspiracy theories that Bart buys, there's a picture on the back of the author. The picture changes several times throughout the episode.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: When Homer and Grandpa are trying to sell the tonic at the mall, when Homer is trying to sell tonic to the Critical Man, all the tonic bottles on the table are actually empty. In the next shot, they're full.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: When Lisa jumps off the tyre swing, her dress is fairly dirty. When Homer drives off, the bottom is dirtier than before.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: At the old Simpson home, Grandpa and Homer run into each other and collide on the porch. In this shot, the windows are dark, but in the next, all the windows are instantly lit up by the fire, which would not be possible in the given time.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: When the janitor shows Marge and Homer into the Utility Room, the only equipment in there is a couple of mops. Later, the janitor comes back and pulls out a big vacuum cleaner that we never saw previously.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: At the retirement home, Grandpa pulls out some medicine from his cupboard. In the next shot, another medicine bottle that wasn't in the previous shots appears.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: In one scene in Bart's treehouse, Wendell's skin is yellow, rather than its usual white color.
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