And Maggie Makes Three - S6-E13
Plot hole: When Homer is seen at work in the flashbacks (before Maggie was born), he is at his usual control panel in sector 7-G, but he only began working here when Burns made him safety supervisor in season 1, "Homer's Odyssey". Before Maggie was born he should have been working at the conveyor belt with the carbon rods, where we saw him in the first couple of episodes.
Shay
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer finds out that he has no Christmas bonus the background behind Marge is the kitchen, but then it cuts to Homer and the background behind him is the kitchen too. (00:08:20)
Continuity mistake: When the cops pin Krusty to the carpet, he moves further away from the yellow stripes between shots.
Other mistake: When Homer and Chief Wiggum fall into the waste, in the second shot, the cliff edge looks very weird. It seems to be transparent with Ruth's car floating in mid-air, and there is a big curved wall that doesn't have ground at the top.
OL1V3R666Kill the Alligator and Run - S11-E19
Continuity mistake: When Homer beats the train they are on a road, but then another train comes by and hits them right where the road was.
Revealing mistake: When everybody is in a big fight at the Do What You Feel Festival, watch out for a man in an orange shirt with black hair. His left eye keeps disappearing for one frame.
OL1V3R666Continuity mistake: When Bart's army is attacking Nelson, there are a lot more kids attacking Nelson than there were training with Bart.
Continuity mistake: When the remote controlled plane crashes into the roof of the burlesque house, it is seen to hit only the side of the roof, yet when Bart goes to reclaim the plane, it is nested on the top of the roof.
New Kids on the Blecch - S12-E14
Continuity mistake: When Homer is pinching Lisa with the "jealousy bug", the sign behind him changes from a gift store to an antique store.
Continuity mistake: When Marge is watching Homer's "Margarine" music video, the coffee in her cup keeps changing.
Jack KaltenbachContinuity mistake: When Homer sits down in the movie theater, all the rows are completely full, including the row behind him. When he turns around to talk to Selma, the seats directly behind him are empty. Then, when Homer turns back to the screen, the Sea Captain and Dr. Hibbert appear sitting directly behind him.
Twotall
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Genesis Tub,' Lisa sits on a tooth-throne in the tub, which has red cloth draped over the arms with gold tassels around the edge. However when Bart comes to take the tub, Lisa stands up on the throne and yells "Bart, no!" In this shot the tassels are gone. (00:17:45)
Hamster
Audio problem: At the theatre, when the cook talks to Mark Hamill off-stage he sounds exactly like Moe the bartender.
Tobin OReilly
Continuity mistake: When Sideshow Bob is shouting and screaming just before he is taken away in a police van, Lisa and Bart swap places right before Bart says "Take him away, boys."
The Simpsons Halloween Special: Tree House of Horror - S2-E3
Continuity mistake: When Homer is preparing the barbecue, he is wearing an apron that says "Mafia staff apron". After he goes to pick up the lighter fluid, it reads "Maffia staff apron", and after he has lit the barbecue, it is back to saying "Mafia".
TwotallPlot hole: In the last part of the episode, when Mr Burns is trying to convince Homer on his float to play a big prank, the timing is totally wrong. Firstly, Lisa sees the writing 'Happy Pranksgiving' on the side of Mr Burns' float way before it reaches her, and it takes Mr Burns ages to change into the Father Christmas outfit.
Lisa's Rival - S6-E2
Continuity mistake: The position of Ralph's Star Wars action figures changes the two times they show his diorama.
Other mistake: There are two mistakes when Bart calls the Krusty Hotline: 1, The cereal box says the phone number is '1-909-O-U-KLOWN.' Bart presses eight buttons on the phone. 2, as he is dialing, you can HEAR seven buttons being pressed. (00:01:45)
Yoshi
There's No Disgrace Like Home - S1-E4
Other mistake: When Homer is at Moe's, there is a boxing match happening on TV. There is a bald guy who is getting considerably battered by the opponent and gets knocked out, and then for some absurd reason he is victoriously standing and smiling as if he had won.
OL1V3R666
Revealing mistake: When there is a zoom in of the house just before Bart gets up late, it has the old arch-shaped windows, but in the rest of the episode it has the normal windows. It's obviously a screen from Season 1. (00:06:00)
OL1V3R666
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