$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: As Marge arrives home and sees the bullet holes in the door, the shot changes to a POV shot from behind the door and you can see there are some changes in the holes. The first change is there are three bullet holes on the right hand side which are all the same distance from each other, when she enters the middle hole has moved closer to the bottom one. The other change is the large hole in the middle of the door. On the bottom right hand side its shape goes from being a little irregular to a more round shape. (00:16:20)
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: When Marge comes home after the bogeyman incident, Homer trips over a footrest. You can see Bart sitting there however his pyjama's are a dark green color when before they were a bright green color. (00:16:35)
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Continuity mistake: When Marge enters the bedroom, the family appears from behind the mattress, and Maggie's outfit is her traditional blue, but when Marge picks her up her outfit is white. (00:17:10)
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Revealing mistake: At the dinner table Homer says something like "as you know it's always been my lifelong ambition to be a blackjack dealer." During this line, for some reason they appear to have used a clip from an older episode (Season 3 / Episode 3 - When Flanders Failed) and dubbed the line over. For one thing, the animation is of a much lower standard than the rest of the episode. And perhaps even more telling, when he says it, he is holding a fork with some food on it, but from the earlier shots we know there is no food in front of him.
Continuity mistake: Near the start when Marge is putting jam on bread, she spreads it on the last piece but as she puts it on the plate it changes to a blob in the middle.
Audio problem: When Homer's vigilante group are putting out a leaf fire, Homer says "No burning leaves without a permit" his mouth is not moving.
Revealing mistake: When everyone is cheering for Ned at the neighborhood watch meeting, Apu's hand is yellow.
Revealing mistake: When Homer is on the news talk-show talking to the cat burglar, he puts his hand on his chest and the opening of his shirt appears over his hand.
Continuity mistake: The man conducting the tour of the box factory tells the children that they will not be able to see a finished box, as the boxes are assembled in a separate location. However, moments earlier we saw a flat box going through a machine, and coming out finished.
Continuity mistake: When Homer is shouting at Skinner about losing Bart, if you look closely you can see that the box with the red cap goes past Homer. However, when he turns round and sees that red cap on a box, that box has already gone by.
Continuity mistake: After Bart's career is dead, he is at his house, and Marge brings out a box of Bart related items. She pulls out a doll and hands it to Bart, as she is handing it to him, the doll's arms disappear, and then reappear when Bart touches it.
Continuity mistake: When Bart is writing from the books in the kitchen, he is seen writing on the paper. In the next shot of him, the paper is clean.
Continuity mistake: In the opening shot of Apu serving his customers, you can see Martin wearing a purple shirt. However, later when all the customers are grumbling about the price, you can see Martin walk away wearing a white shirt.
Continuity mistake: Apu grabs the ham and crosses out of the expiration date with a thick black marker. When he places the ham on the shelf the black marker cross out is gone and the writing on the pack looks perfectly printed as before.
Revealing mistake: Apu's moustache disappears for some seconds after having his name tag removed.
Continuity mistake: When the robber shoots Apu, he is shot around his leg. In the next shot, the wound is in his chest.
Lisa vs. Malibu Stacy - S5-E14
Continuity mistake: During both conversations Lisa has with the real Stacy (the creator of Malibu Stacy), her drink magically refills itself a number of times.
Lisa vs. Malibu Stacy - S5-E14
Continuity mistake: When Lisa and Marge go on the tour, when the film has finished the woman turns it off with a remote controller and puts it behind her back. In the next shot from behind her it isn't in her hands and there is no sign of a pocket or any indication she put it anywhere else.
Lisa vs. Malibu Stacy - S5-E14
Revealing mistake: When Lisa says "Now all we need is a name", Maggie's head disappears for a split second right before the shot changes to Bart talking.
Lisa vs. Malibu Stacy - S5-E14
Continuity mistake: When the Simpsons are leaving the house to go to the mall. The aerial shot shows that they are leaving in Marge's red station wagon, but the very next shot of them in the car shows that they are in Homer's pink sedan. The shot of the station wagon leaving is probably a re-used shot from a previous episode.
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