Sleeping with the Enemy - S16-E3
Continuity mistake: When Lisa is talking to Homer at the start, we see that Homer puts his Duff down on the table, yet for the rest of the scene it isn't there. (00:01:15)
Treehouse of Horror XV - S16-E1
Continuity mistake: When Lisa goes to see Comic Book Guy, we see that he places the dagger on the table in the centre of the green thing, then when the shot changes and he puts the comic there the dagger is gone. (00:09:45)
Continuity mistake: When Homer is sleeping on Bart's school floor, Bart puts his shoe in Homer's mouth. Later, when Homer is screaming about "Cobras," the shoe has been coloured black, rather than the usual blue.
Continuity mistake: When Lisa knocks the lamb chop out of Bart's mouth to Homer's it changes colour during the journey.
Tree House of Horror X - S11-E4
Continuity mistake: When The collector falls over the banister and into the Lucite, Xena is taped into a plastic pouch; but when she gets out, she pulls the bag down easily, without ripping open the bag or the tape.
Continuity mistake: While Krusty is describing his prostate to the children, the green umbrella vanishes from beside Lisa. (00:07:40)
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.
Homer Badman - S6-E9
Continuity mistake: Just after Marge's left jacket pocket bursts open at the candy convention the shot changes to a shot of Marge's face. The next shot her right pocket has suddenly burst as well and the candy in it is no where to be seen.
The Boy Who Knew Too Much - S5-E20
Continuity mistake: During the trial, when Freddy Quimby's lawyer is asking him to come to The Front, the flag to the right of the judge disappears during one shot. (00:13:40)
Homer Alone - S3-E15
Deliberate mistake: Arnie says that he drops his bagel. When he does he starts to say it, but when we see the helicopter it has just fallen out. If he dropped it at the time he did, then it would be much further down and wouldn't be visible in that shot. (00:05:20)
Itchy and Scratchy and Marge - S2-E9
Continuity mistake: In the beginning after Maggie hit Homer on the head, it shows him laying on the couch with Bart & Lisa on the left. The next shot it shows the TV, in the next shot it shows Homer on the left sitting and Bart & Lisa on the right. It's impossible for Homer to get up and switch sides with Bart And Lisa in less than 5 seconds.
Catch 'em If You Can - S15-E18
Continuity mistake: The Credit card numbers for Ned and Rod's VIZA cards are exactly the same: 8525 4941 2525 4158 First Bank of Springfield Viza valid from 1/1 to 12/31(thirty years on the credit card?)
One Fish, Two Fish, Blowfish, Blue Fish - S2-E11
Continuity mistake: Just after Homer says, "This fish is delish", one of the pieces of sushi keeps reappearing every time Homer eats it.
Continuity mistake: Chief Wiggum's badge is shown to disappear under his fat in one scene, but in the following shot of him the badge is completely visible.
Weekend at Burnsie's - S13-E16
Audio problem: There is an elaborate bass line right at the end of Phish's song; however, the bassist's fingers don't even move. There's no way he could play that line without moving his hand. (00:13:50)
Continuity mistake: When Bart falls off his skateboard after attempting to skate over Homer's car, as the shot zooms out you can see his board is nowhere to be seen. (00:11:05)
Continuity mistake: When Homer reaches into the fridge to take out the tub of triple chocolate ice cream, we see it in a brown and white striped tub. When he lifts it out, it's turned into a plain pink tub and has shrunk considerably. (00:03:50)
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: While hiding the fact they are looking at sex books from Bart and Lisa, Homer picks a green book. When we see what he's reading, it's a grey "Maple Thorpe" book.
Continuity mistake: As Milhouse walks up to the TV to turn up the volume, Lewis is nowhere to be seen in a wide shot, but as Milhouse walks back over to the couch you can see Lewis sitting on the floor. (00:02:15)
Factual error: When Bart is trying to escape from the girls at the start, Bart's door opens into the room. This would mean the hinges would be inside Bart's room and the girls couldn't have been able to remove them.
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