Continuity mistake: When Chief Wiggum pulls Homer over for speeding, all the clown decorations on his car have disappeared.
Continuity mistake: When Bart and Lisa are looking at the globe, Bart points out Argentina and 'Ran McNally.' 1) Next time you see the globe, it is showing Africa and Asia 2) Asia is shown incorrectly and 3) The equator has disappeared.
Continuity mistake: When Homer is threatening to boot the Prime Minister, he is holding him still with his left arm. When the shot goes to behind Homer, he has his right arm on the Prime Minister's shoulder. When the shot cuts back to a direct view of Homer, his right arm isn't touching the PM.
Continuity mistake: Two guards take down and eat the embassy flag. But when the Simpsons look down at the frogs at the embassy, the flag is still up on the pole.
Continuity mistake: When Bart is trying to get the toilet water to flow the other way, the toilet can't refill that quickly with that number of flushes.
Continuity mistake: When Bart is trying to make the toilet water flow the other way, in one of the flushes the toilet begins to dispense water before Bart pulls the chain.
Continuity mistake: Bart and Homer escape from the court by jumping out of a window, however in the next shot they are running away from the door as if they escaped via the doors.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Marge says, "I wish you wouldn't put Homer down like that.", Patty and Selma's dresses swap colour between shots.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When one of Marge's sisters says, "He blew all your savings on jack o'lanterns.", one of the armrests on the sofa is black for some reason.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Homer for the second time throws out Patty and Selma, the knocker just stays in the same place as if the door hasn't opened at all. (It looks like it is floating in mid-air).
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Homer tries to tell Marge how he did in the test, Selma and Patty are holding their cigarettes. In the next shot, the cigarettes are in their mouths.
Homer vs. Patty and Selma - S6-E17
Continuity mistake: When Homer is walking upstairs after kicking Patty and Selma out for the second time, the wall that Homer was approaching is a darker colour than it usually is, and Homer walked up the stairs slowly. But a second later he closed a door, indicating that he went into a room. Are we really to believe that he could go very quickly from the stairs to a room in a matter of seconds?
Homer vs. Patty and Selma - S6-E17
Continuity mistake: At the beginning of the episode, there is a drunk wearing glasses. He disappears in the next shot onwards.
Continuity mistake: When Wolfcastle says that 'Jay Sherman insulted him, now he will die', for a few shots the shadows are on the floor before they magically disappear. Also, the shadow of the gun does not match the real gun.
Continuity mistake: When the Simpson family and Jay Sherman are having dinner, things like the food from their plates, their knives and forks and even Homer's burping trophy disappear and then reappear for a couple of seconds before disappearing again.
Continuity mistake: When everybody is chanting 'Film Festival', you can see that Mayor Quimby has his arm up. But in the next shot, which changes so that you can see Marge, he his holding up his other arm.
Continuity mistake: When wedding has been just called off, Lunch Lady Doris calls everyone for wedding cake, and among people who rush to it we can see Moe (you can recognize him by his eyepatch), then, Lisa starts to walk off and among the people she passes by you can see both Lunch Lady Doris and Moe.
Continuity mistake: By the vending machine, Lisa first points her card at the cell on the right, then there's a zoom on the cells and we see her hand starting to point again, but this time at the cell in the middle. In the next shot, she lowers her hand with the card, which however in this shot is pointing at the cell on the right again.
Continuity mistake: When we first see union flag on fire, the flames are already consuming over the half of its upper edge. Then when we see it reflected in Hugh's eyes, no more than a half of the edge is burning.
Continuity mistake: When Lisa enters the taxi and we see the door being closed, the camera turns into the full view of the taxi in the next shot, and now we see that the door (the one with company logo on it) has changed its shape 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