Continuity mistake: At the Penitentiary gates, Nelson's position changes between shots. The whole group are near the gates, then far away, then Nelson is separate from the group when he throws the key.
Continuity mistake: In the scene where the bullies are talking to Bart and Ralph on the street corner, they move positions between shots. They change from a straight line to being in an arc shape, to being in a group.
Continuity mistake: In the scene in Ralph's bedroom the nightlight changes positions between shots. First it's far away from the doorway, then near to it, then right next to it.
Continuity mistake: When Bart and Ralph are in the prison and see the key, the window's shadow is of four squared panels. When they go to pick the key up and the rat takes it the shadow shows 3 rectangular panels.
Audio problem: When the family are about to enter the Knowledgeium Homer says 'Will there be beer?' but his lips don't move.
Continuity mistake: In the Wiggum's house the parent's bedroom changes style several times. When it is first seen the cupboard is opposite the door (When Chief Wiggum is looking into the room after climbing the stairs). Then it is on the wall running across from the doorway later when Chief Wiggum enters the room. When the Chief puts the Police Master key on his bed post the doorway is behind the bed and the bed is opposite the cupboard. Later when Bart steals the key the bed is seen parallel to the doorway.
Continuity mistake: After Bart and Ralph have just visited the cake shop they have chocolate and icing all around their mouths. Also they are carrying the 'Newly Weds'. In the next shot where they walk around the corner the chocolate, icing and model bride and groom have all disappeared.
Continuity mistake: At the Penitentiary, Jimbo's video camera appears and disappears from nowhere. He isn't seen carrying it on him.
Continuity mistake: When Mr Burns opens the note from the rocket he places the rubber band on his desk. In a following shot the rubber band changes position.
Continuity mistake: In the scene at the abandoned Penitentiary the puddle which Ralph and Bart fall into just appears from nowhere.
Continuity mistake: When the family are on the conveyer belt in the Knowledgeium, Homer turns round and grabs the handrail (after the Troy Maclure announcement) and his fingers are just touching the rail. In the next shot his hands are clasped to the rail.
Continuity mistake: At the end of the episode when Mr. Burns rotates his desk to turn off the power, the ink block and fountain pen to his left change position.
Continuity mistake: When the family are walking through the car park after the visit to the Knowledgeium they walk by a purple car and there is a quick visual of a blue car in the bottom left hand corner of the screen.They immediately stop and they are now next to a pink and brown car.
Audio problem: At the Penitentiary gates when Ralph says 'Daddy's key went in there,' his lips don't move.
Continuity mistake: When Ralph and Bart are playing cards, Ralph has four cards in his hand. In a following shot he has five then back to four cards again.
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: 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 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.
Continuity mistake: When Bart and Ralph twist the key into the armed switch, the armed sticker is red and the off sticker is yellow. Then, during the press conference, the stickers switch colors. Then, when Mayor Quimby sits in the electric chair, they switch back.
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