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 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.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: In Homer's flashback, when the pimp chases Homer, who is covered in garbage, Homer runs away from him on one side of the street. When Homer runs on the other side of the street, he is not covered with garbage. When he climbs a ladder and falls into a manhole, he is covered with garbage again.
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: During Homer's flashback, Homer passes the sign that says "Jeremiah's Johnson" twice.
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.
Lisa's Sax - S9-E3
Continuity mistake: In the episode 'Lisa's Sax' (season 9, ep. 3), King Toot's music store is across the street from Moe's Tavern. However, in numerous later episodes, there are stills of Moe's Tavern that show King Toot's music store next door, not across the street as in the aforementioned episode.
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.
Tree House of Horror VIII - S9-E4
Continuity mistake: Mutant Moe had one red mark on his face wile talking to Homer in the church, but when everyone attacks him, he has two.
Tree House of Horror VIII - S9-E4
Continuity mistake: Homer is dancing naked in the church and has his pants on the pew. There is then a wide shot and his pants are gone.
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.
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.
Continuity mistake: At one point Marge says "no guns at the dinner table" and Homer says "you said the breakfast table", then Marge replies "it's the same table". In most episodes they eat dinner at a different table.
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.
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.
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.
The Two Mrs. Nahasapeemapetilons - S9-E7
Continuity mistake: The amount of liquified chips in the bag at the home changes depending on the shot.
Continuity mistake: When the "Angel" tells everyone to prepare for the end, Carl is seen with yellow skin.
Continuity mistake: While everyone in Springfield is waiting for the apocalypse, Dr. Hibbert's wife Bernice is seen with yellow skin while she's holding on to him.
Continuity mistake: When Dr. Gould says the DNA test was inconclusive, Apu is seen in the background with yellow skin.
Continuity mistake: During the scenes at the site of the mall during the part where they find the Angel, Skinner's hat disappears and reappears.
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