Tree House of Horror III: The Simpson's Halloween Special III - S4-E5
Plot hole: At the theatre in the "King Homer" bit, the audience are treated to a traditional showgirl spectacle. But the girls have no curtain behind them, and so the audience should have seen Homer the ape, but they act completely surprised a minute later when Homer comes on. (00:11:40)
Lisa's Pony - S3-E8
Revealing mistake: At the end, Homer and Lisa don't cast a reflection on the Kwik-E-Mart's doors. They should, since they are only a few metres from it.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: When Homer enters the bar, you briefly see that Lenny has dark green braces and a fawn coloured shirt. The next shot, they switch colours.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: At one point, Lisa and Bart are watching fireflies through the window. When Homer comes in, the fireflies are gone.
Wild Barts Can't Be Broken - S10-E11
Audio problem: When Lisa is broadcasting secrets about Springfield residents in a British accent, her lips don't match her mouth at all.
Sunday, Cruddy Sunday - S10-E12
Continuity mistake: When Homer gets the coupon book, look at the plant on the wall. It changes position between shots.
Sunday, Cruddy Sunday - S10-E12
Continuity mistake: The desk in the car repair shop behind Homer changes positions between shots.
Audio problem: At the end where Homer is carrying Mark Hamill out of the theatre, Mark's lips don't match with what he's saying.
When You Dish Upon a Star - S10-E5
Revealing mistake: When Homer and the family are having hamburgers at the dinner table, at one point you can see the oven. The pointer on one of the dials is misaligned.
Revealing mistake: When Skinner talks to Otto on the bus, the point of his hair is touching a pole. Look at the pole - Skinner's hair is going through it.
Bart Carny - S9-E12
Continuity mistake: When Cooder comes out of the house to witness Homer throwing the ring onto the chimney, there's a doorbell on the side of the doorway. The next shot, it's disappeared.
Continuity mistake: When Homer is fishing, the colours of the things on his hat switch places between shots.
Continuity mistake: When Frink collapses at the table, his sleeves are green. When it cuts to a wide shot, they are yellow.
Continuity mistake: When Bart and Lisa are in the compound, just before Bart gets brainwashed, the bags that were behind Lisa disappear. Homer and Marge were on the other side of the room, so they couldn't have picked them up.
Bart Carny - S9-E12
Factual error: Sharks cannot just reverse backwards like that one did under the glass bottom boat. The only way sharks can go backwards is either swimming around in a circle or allowing the current to carry them.
Lisa's Sax - S9-E3
Plot hole: In this episode, Homer repeatedly says that they have no air-con or thermostat, but we saw that they had a thermostat in the first clip show episode. What happened to it?
Bart Carny - S9-E12
Continuity mistake: When Homer is talking through the door to Cooder about getting the house back, the shot is through the fisheye lens on the door and you can see Marge, Bart and Lisa smiling. The very next shot, they suddenly have a frown in no available time.
Other mistake: When Homer is muttering whilst walking up and down the home landing at night after being told he has to wait 5 days to receive his gun/license, Lisa being awoken by his muttering complains that it is 3am but her bedside clock shows 9.50/21.50. (00:06:55)
Gal of Constant Sorrow - S27-E14
Continuity mistake: When Homer returns from work to get the cat out of the plug socket, he removes the plug socket cover without removing any of the plugs, but when Homer realises that the cat is in the ceiling, both the plug socket cover and the plugs have now been removed from the wall.
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