Continuity mistake: As soon as the family has left the Knowledgeium, they are immediately outside walking away. The shot changes and the building is nowhere to be seen.
Audio problem: When Bart is reading Marge's police file he says 'Oh, Mum's only been in twice.' But the lip sync is a bit out because it does not match the words he says.
Continuity mistake: Bart turns the door handle to the joke shop and a boxing glove comes out through the door and hits him. But when he opens the door there is nothing on the other side for the glove to come out of.
Bart Carny - S9-E12
Continuity mistake: Up until the point at which Skinner starts throwing rings at the block in front of the Spanish lamp, the block simply doesn't exist. It only appears once he starts throwing the rings.
Continuity mistake: When Chief Wiggum finally climbs the stairs his gun is visible to be a black, old style revolver with a curved handle. In the next shot where he draws his gun, it is a grey, new style handgun.
Continuity mistake: When Homer is running down the street with his garbage, it spills out all over the road. But in the next shot when the garbage men are confronting him, all the garbage is gone.
The Two Mrs. Nahasapeemapetilons - S9-E7
Continuity mistake: The amount of liquified chips in the bag at the home changes depending on the shot.
Continuity mistake: When the family are on the conveyer belt at the beginning the family are travelling along. In the next shot (the close up) they are travelling alot slower.
Bart Carny - S9-E12
Continuity mistake: When the Simpsons drive up to the house, there are no boards on the window. When they can't get in, suddenly there are boards on the windows.
Realty Bites - S9-E9
Continuity mistake: While Homer is driving Snake's car, he passes a place called Heinrich's Monocle Shop three times.
Continuity mistake: In the scene at the United Nations, the Russian placard is just a placard. In the next shot, the placard is attached with a rod to rotate it at the push of a button.
Tree House of Horror VIII - S9-E4
Continuity mistake: Homer is dancing naked in the church and has his pants on the pew. There is then a wide shot and his pants are gone.
Realty Bites - S9-E9
Continuity mistake: The Front door of the Murder House has two windows which vanish, and also a door knob that switches sides so the door opens the opposite way.
Realty Bites - S9-E9
Continuity mistake: Snake has an earring in his right ear, but in some shots the earring is missing then reappears, or it switches to his left ear. Also, when Homer and Snake are fighting on the hood of the car Homer's right shoe falls off, but when the car speeds toward the Murder House, Homer is wearing both of his shoes while he and Snake are still fighting on the hood.
The Trouble With Trillions - S9-E20
Continuity mistake: In the post office when Chief Wiggum is using the megaphone, Otto is seen in the right line as seen from the door but when Kent Brockman attempts to interview him he is magically in the other line, in front of Krusty.
Revealing mistake: When Marge stands up at one point in the airplane restaurant, her legs and part of her dress have disappeared.
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.
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