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.
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.
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: When Homer's head gets caught in the middle of the draw bridge, a yellow stripe can be seen down the center of the bridge (where Homer has become stuck). However, in the closeup of Homer being hit by the cars, the stripe has disappeared.
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.
Miracle on Evergreen Terrace - S9-E10
Continuity mistake: When Bart pulls the melted tree out of the house, a shovel appears out of thin air so he can shovel snow onto it.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: At the very start of the episode, Moe is wearing a watch. But in the next shot when all the guys come in, and all following shots, the watch is gone.
Tree House of Horror VIII - S9-E4
Continuity mistake: When Homer pulls up to the stoplight, the number of cars in front of him changes. When he first stops, there are 3. When he gets out of the car, there is only 1.
Continuity mistake: In the scene when Homer is signing up for the naval reserve, the administrator gives him a pencil to fill out his form, but when the camera moves to The Front of Homer it changed to a pen.
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