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.
The Trouble With Trillions - S9-E20
Continuity mistake: In the scene where Homer is eating a hot dog just before the post office closes for the day, the vendor behind the hot dog cart has a apron over his shirt. The very next shot the apron has disappeared. (00:05:05)
The Trouble With Trillions - S9-E20
Deliberate mistake: When Homer is being interrogated by the IRS, his package is briefly replaced by a ball of string when the IRS agent sits down in the chair and spins around.
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 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.
The Trouble With Trillions - S9-E20
Continuity mistake: The To Do Pile doesn't appear until Marge mentions it.
The Trouble With Trillions - S9-E20
Continuity mistake: In the scene where the FBI agent and Homer are going into the photo booth to view the video, look to the right of the photo booth before they enter. There is a white cup next to the booth. After they have watched the video and are standing outside the booth talking, the cup is now red instead of white.
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.
Continuity mistake: When we see the wide shot of all the houses going along the road, you can see that Moe's door is facing away from the Simpson's house. But in the next shot, Homer jumps in through Moe's door, it's like the tavern did a 180 degree turn.
Continuity mistake: At the garbage man debate, when Homer says 'Then you should have been early.', we see a shot of Lenny laughing. To the right of him, there is an old woman. In the next shot of Chief Wiggum, the same old woman is sitting to the right of him. In the later shot of Wiggum, Miss Hoover is sitting to the right of him and the old woman has disappeared.
Continuity mistake: When Ray Patterson's / Homer's office is shown, the text on the door is different according to the different shots. When the shot is on the door, the writing on the window (Name and Sanitation Commissioner) is close together, but when the shot is from inside the office with the door open, the writing is apart.
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.
Audio problem: In the U2 scene during the end credits, when The Edge says "oh, here we go" his mouth is not in sync with his voice.
Continuity mistake: At one point when Homer is giving his speech in front of the Jebediah Springfield statue, Carl's skin is yellow. In all other shots he is back to his normal color.
Continuity mistake: At one point, while everyone is clapping for Homer during the debate in The Town hall, Apu is seen with yellow skin, and Chief Wiggum is seen with black hair among the townspeople. In all other shots, they're back to their normal skin and hair color.
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: 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.
Revealing mistake: When Homer pushes over the windmill something comes off and chops the head off a metal figure, but the head comes off before hit. (00:16:05)
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