Audio problem: When Michael and Bart are playing a song to Lisa, Bart uses her bin as a drum. Sometimes you hear tapping, but Bart doesn't touch the bin.
Continuity mistake: The text on the billboard which says "She's having a baby...again!" is black when Mel Gibson and Homer crash through it. After they have landed on the ground, the text on the billboard is white.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Luke jumps off of the horse to save the rattlesnake egg, the horse changes from being beside Luke to beside Lisa between shots.
Continuity mistake: When the family are driving home from the cinema, Bart draws an angry face on the back of Homer's head. It is never there at any other point in that night.
Continuity mistake: When we first see the medicine cabinet in the Simpson's bathroom the hinges are on the left. When Homer pokes it with the wire it opens as if the hinges are on the other side. The last time we see it, when Lisa rescues Maggie, the door is missing altogether. (00:01:25)
Continuity mistake: Near the beginning when the family is eating dinner, the glasses on the table keep refilling/emptying themselves, even though nobody takes a drink. (00:03:40 - 00:04:30)
Bart's Friend Falls in Love - S3-E23
Continuity mistake: When Lisa is explaining about subliminal tapes to Homer, there is a robot on the cover of the magazine, whose helmet is yellow. But in other parts of the episode, it is grey.
Continuity mistake: In the video store, when Homer looks at sports tapes, the categories of movies behind him change from drama, horror, and 'Elvis' to drama, western and horror. (00:05:55)
Other mistake: When Homer is crossing the rickety bridge in the snow plow there is no snow on the planks even though he is in a blizzard and the storm couldn't have just started because the path he just came from was covered in snow. (00:18:55)
Marge Simpson in 'Screaming Yellow Honkers' - S10-E15
Continuity mistake: After Marge pulls out of the Store, she gets stuck at a traffic jam. But when she does pull up, all of the groceries in the back have disappeared.
How I Spent My Strummer Vacation - S14-E2
Continuity mistake: When everyone is getting guitars, Homer is among the people who are waving their hands to get one but in the scene before it, when they are in the cabin, Homer already had one.
Factual error: The Suburb of Wooloomooloo where the chase starts is in Sydney, and the Simpson family are chased all the way to the American Embassy which is in Canberra, a distance of at least 150 kilometres. That's some impressive running, especially for Homer.
Continuity mistake: At the beginning, if you watch the clock as Homer walks in, the time changes between shots. (00:01:30)
Audio problem: When the old lady is playing the keyboard at Homer and Marge's wedding, her hands don't match the music.
Revealing mistake: On the original DVD version, when Bart says to Lisa "I didn't want you to wreck your life" the screen is cut off on the right side slightly. (00:20:25)
Continuity mistake: When Bart is digging his hole, Homer goes over and starts talking to him, and you can see a spade standing up outside of Bart's hole. The spade wasn't there in the previous shot of Bart digging. (00:02:05)
Continuity mistake: This episode rewrites the entire backstory of Marge and Homer. For starters, Lisa and Bart were both not born yet, despite the fact that in the episode "Lisa's First Word," the '84 Summer Olympic games were being broadcast, and Bart and Lisa were both there. In this episode, Homer and Marge were just dating, but again in "Lisa's First Word," they were married and living in their Evergreen Terrace house. Additionally, Maggie was born in the episode "And Maggie Makes Three." Homer also lost all his hair in that episode, yet in this episode in the early 90's he still has a full head of hair.
Continuity mistake: When Lisa finds the doorbell Marge wanted and she plays it, it is gold, but when Marge picks it up it is grey-ish.
Continuity mistake: As Marge is feeding Maggie a grapefruit, Bart takes out his bongo drums and plays them. Watch as Bart plays - the shot zooms in from the back of Bart towards Maggie, and you can't see Marge in the scene sitting close to Maggie; the next shot shows her though.
The Two Mrs. Nahasapeemapetilons - S9-E7
Continuity mistake: The amount of liquified chips in the bag at the home changes depending on the shot.
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