Tree House of Horror VIII - S9-E4
Other mistake: In 'Homega man', Homer goes into the bomb shelter and does not shut the door, and you can still see it open for a while after he is in there. Herman does not close it behind him - you can tell by his skeleton's position. But Homer opens the door to leave the shelter after he has eaten the food, and it must have been closed for him to have survived the atomic attack, because it vaporised Herman, who was only a few feet away.
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.
Bart Carny - S9-E12
Continuity mistake: At dinner when the carny dad is doing his cigarette trick, the shot changes to Bart and Lisa and they have piles of food on their plates. About 10 seconds later Marge gathers the plates up and there is nothing on them. Are we to believe that they ate all this food in such a short space of time?
Continuity mistake: When Flanders walks up to the door, there is nothing next to the door, but in the next shot after Homer has thrown garbage onto him, there is an egg box next to the door.
Continuity mistake: When the garbage man is asking Homer if he learned anything from love day, his cigarette is in his hand, but in the next shot when Homer says, "That was yesterday moron", the cigarette is now in his mouth.
All Singing, All Dancing - S9-E11
Continuity mistake: In the scene where Snake first comes in to shoot the Simpsons, after they sing, he starts singing. When turns his head then turns it back, he blinks and his eyes disappear.
Continuity mistake: After Apu & Homer find Jasper in the freezer. Apu removes a note from his hand. Minutes later Dr. Nick walks in the door you see Jasper still holding the note then disappears again when Dr. Nick opens the freezer door.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: Just before Duff man arrives, Barney has loads of sweat on his shirt. But when Duff man pushes the big jug of beer towards him in the next shot, the sweat is gone.
The Trouble With Trillions - S9-E20
Continuity mistake: When Homer is watching TV early in the episode, he has a watch on his left wrist. When he begins working on filling out his tax forms, the watch has disappeared. When he takes down the sailboat painting from the wall, the watch has returned.
Audio problem: When the family are about to enter the Knowledgeium Homer says 'Will there be beer?' but his lips don't move.
The Trouble With Trillions - S9-E20
Continuity mistake: When the FBI agents arrest Mr. Burns he is handcuffed; however, when Mr Burns is being dragged off there are no handcuffs on his wrists at all.
The Two Mrs. Nahasapeemapetilons - S9-E7
Continuity mistake: When we see the garden and Bart throwing Hymns into the fire the large tree is fully green. After the shot of Bart,the camera goes up and we see branches with no leaves on them though.
Bart Carny - S9-E12
Continuity mistake: When Bart starts Hitlers' car moving, for a couple of shots the "Iron Cross" disappears from the side of it.
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 the Home security seller is first seen, he steals an ashtray and a remote control off a speaker and turntable player both close to each other, When the shot changes the speaker and turntable player are much further away from each other.
The Two Mrs. Nahasapeemapetilons - S9-E7
Continuity mistake: When Apu walks down the isle the early shots show that Bart and Lisa are not amongst those either side.When Apu walks by,the shot goes to the ground and they have now appeared.
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.
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