The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: Just before Homer tries biting off the boot, he is wearing a watch. But from then on it disappears off his arm until he is trying to figure out how many hours it is from 9-5.
The City of New York vs. Homer Simpson - S9-E1
Factual error: The windows of the World Trade Center couldn't open and the Twin Towers weren't in front of each other as depicted in this episode. They were at an angle.
The Two Mrs. Nahasapeemapetilons - S9-E7
Audio problem: When Homer is running for the food, after racing in the wheelchair with Jasper, he says 'Eat my dust' but his lips don't move for the 'my dust' part.
Continuity mistake: The right handle plate on Homer's gun is fastened with two screws throughout the entire episode. But in the scene where he promises Marge to get rid of the gun and they hug in the kitchen, the gun is seen lying on the table with only one screw in the handle.
Audio problem: After Homer and Marge steal Gil's balloon, they fly towards clothes, Marge says "Clothes! We're saved!", but her mouth dosen't move.
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.
Lisa's Sax - S9-E3
Continuity mistake: When Bart is standing on the bench, Jimbo and Milhouse are standing in The Front row, on the right side of the screen. But when there's the closeup (a second later), there are children shown in front of Jimbo and Milhouse and the girl with the purple hair is gone.
Realty Bites - S9-E9
Continuity mistake: When the real estate team learn that Marge has sold the murder house, Marge is wearing a red blazer but in the shot which faces Marge's back the blazer is missing, then in the next shot Marge is wearing the blazer again.
The Two Mrs. Nahasapeemapetilons - S9-E7
Continuity mistake: When the garden is seen with Bart throwing Hymns into the fire Apu's mother starts to walk to him and she must walk through a curved green structure.In the next shot of Bart,the structure has gone.
Continuity mistake: When Homer is at Moe's tavern talking about Marge, the level in his beer glass keeps changing even if he doesn't drink.
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.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: When the camera pans down the Trade Center, there is no washing line there. But a few shots later, a washing line appears.
Realty Bites - S9-E9
Continuity mistake: When Marge finds out the Mr Hutz does real estate, the 'For Sale' sign changes from black to red and then back again.
Bart Carny - S9-E12
Continuity mistake: When the Simpsons are cleaning their house, the painting above the chair goes from a picture of Maggie to a picture of a boat.
Bart Carny - S9-E12
Continuity mistake: In the end of the episode when the family has reclaimed the house and are cleaning up the living room. As Homer mentions about letting the Cooders stay, Bart tells Marge to get him away from the window. She is standing right next to the couch in the lounge but the very next shot she lowers her hands and pats the couch yet is now in the family room. (Note: There was a few shots that showed there was two couches so the mistake is with Marge suddenly moving not the couch.).
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)
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.
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)
Continuity mistake: The offensive baseball cap that is in the Kwik-E-Mart changes from green to blue during the episode.
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