Continuity mistake: In Moe's, Homer points at Lenny and says "Are you calling me a liar," with the same hand which is instantly holding a beer in the next shot.
Continuity mistake: When Homer opens up his bar there are 4 cars parked outside, but later when Moe opens the garage door there are no cars, but no one has left.
Hunka Hunka Burns in Love - S13-E4
Continuity mistake: In one of the shots after Mr Burns has broken the fortune cookie, the remains of it vanish from the table. There is something else on the table, nearer Smithers, but it and the cookie are very different shapes, so it's very difficult to confuse the two.
Hunka Hunka Burns in Love - S13-E4
Continuity mistake: When they are sitting down in Stu's Disco, there is a little glass next to Mr Burns' glass which vanishes in later shots.
Hunka Hunka Burns in Love - S13-E4
Audio problem: When Marge says "New underpants?", she is mouthing "New boxers?"
Continuity mistake: When Homer is being hypnotised, in some shots there are plates on the Simpsons table, in others there are not.
Continuity mistake: At the end of the episode, Homer puts a skull in a box on the coffee table. When Moe arrives to explain his theory, first the box disappears from the coffee table, then the entire table vanishes.
Continuity mistake: When Homer first finds the corpse, there is no belt on the trousers it is wearing. But in the shot where Homer starts to scream, there is a belt on the trousers.
Continuity mistake: When Marge throws the Burly paper in the water, they start growing and sucking up the water. But the things inside that rolls don't grow.
Continuity mistake: When Homer first lifts the corpse up, it is wearing glasses. But when it cuts to the shot of the corpses' face, the glasses have gone.
Continuity mistake: When Homer's Vegas wife shows him the video in front of Marge, it shows Homer kissing Ned. This didn't happen when she showed it in the Vegas episode.
Continuity mistake: During the scene where Grandpa is getting married to Amber, his reading glasses appear from nowhere.
Continuity mistake: When the family are returning from the picnic, they pull into the drive and Homer has a seatbelt on in some shots, and in others he isn't wearing it. You can't even see it attached to the side of the car sometimes.
Sweets and Sour Marge - S13-E8
Continuity mistake: When Lou throws a small chocolate statue in the fire, his skin is yellow when it is usually brown.
Sweets and Sour Marge - S13-E8
Continuity mistake: When Homer falls off the human pyramid, he grabs onto someones rear end to stop himself from falling. In the next shot, he is suddenly holding a foot.
Sweets and Sour Marge - S13-E8
Continuity mistake: When Homer dumps the sugar into the ocean, the hand pressing the "dump cargo" button has a yellow shirt cuff. Homer is wearing a white short-sleeved shirt.
Sweets and Sour Marge - S13-E8
Continuity mistake: At court, when Garth Motherloving tells Judge Snyder "I'll kill you while you sleep", the blue haired lawyer's suit is green. His suit is grey in all other shots of him.
Continuity mistake: In the cinema, it is clear that the people attending the movie keep on changing. For example, For a few shots, you can see that Krabappel and Skinner are sitting in The Front row, but the next time you see those seats, they have been replaced by Lenny and Carl and Krabappel and Skinner aren't in sight.
Continuity mistake: When Marge and Homer are at the Springfield formal ball at the Country Club, about half way through the ball, there is a woman with her back to the camera as she is talking to Marge and Homer. Homer is on Marge's left side. In the next shot when Marge's back is to the camera and you can see Marge still talking to the woman, Homer is no longer on Marge's left side, he is gone.
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