Sweet Seymour Skinner's Baadasssss Song - S5-E19
Continuity mistake: In the air duct, the dog comes up behind Willie in a straight line and licks his feet, we saw what the duct looked like when Willie turned around. However, when the children start throwing stuff at the duct, from the outside there is a sharp bend right behind where Willie and the dog are that wasn't there in the internal shots.
The Boy Who Knew Too Much - S5-E20
Continuity mistake: Hans Moleman's clothes change from white to black during the trial. (00:12:05 - 00:13:25)
The Boy Who Knew Too Much - S5-E20
Continuity mistake: The American flag at the judge's right transforms to a plain white flag during the trial. (00:12:50 - 00:13:25)
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)
The Boy Who Knew Too Much - S5-E20
Factual error: Apu (an immigrant from India) could not have been selected for the jury because he is not an American citizen, and this was before he became a naturalized citizen in "Much Apu About Nothing".
The Boy Who Knew Too Much - S5-E20
Continuity mistake: When Homer and Bart see each other skipping work/school, Homer is eating a donut then drops it on the pavement when he sees Bart. In the next shot of both of them the donut has disappeared.
Continuity mistake: During the wedding, when seen from behind Reverend Lovejoy, there is no podium in front of him (although his hands are poised in mid-air as though one should be there). In the reverse shot, the podium has magically reappeared. (00:20:00)
Continuity mistake: When the person delivers the animation cell, his skin changes from white, to brown and then back to white. When Bart looks through the letterbox to see who was there, his skin is white. When he gives the box to Bart, it is brown. When he hits Bart in the face and says "that's for keeping me waiting", it is white again.
Continuity mistake: The cake that Marge bakes for Homer is initially white, but pink icing instantly appears on top between shots.
Continuity mistake: During the wedding you can see in the background Apu and Sanjay but Sanjay's skin is yellow.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Homer gets thrown out of the house by Marge and Otto walks up to him, you can see that it is Smithers and Carl standing behind Homer. Yet in the next shot when you see Homer's face, it is now Principal Skinner and Carl standing there.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Marge is shopping at the Kwik-E-Mart she puts a red can and a blue can on the counter.When Apu tells her about the offer on hair dye he puts two blue cans into the paper bag.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Homer comes into the kitchen he is holding a pipe in his left hand. But in the next shot you see him holding up the ruined jacket with his left hand, then in the next shot his hand is back in his pocket.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Homer wipes the tobacco on his forehead in his new class, the tobacco just disappears on his hand/sleeve.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: Marge puts down 2 glasses of juice and a baby bottle on the table when she is telling the kids about the marriage problems. but when she walks away in the next shot, the glasses and bottle are gone.
Secrets of a Successful Marriage - S5-E22
Continuity mistake: When Homer sees Marge and Moe near the end, the coffee table changes size between shots. It's large when Moe sits on the couch.It's smaller when there's a shot of Homer and long again when the high shot shows Homer walking out (when his rags are stuck on it)
Factual error: When you see Ned Flanders put the earth back inside the hole, he puts it back in much faster than is possible. In one shot, he is only just starting to put it back in, then you see Bart who talks to himself for a few seconds, then back to Flanders, who has finished burying what is later to be revealed as the plant that he (Ned) drowned.
Continuity mistake: In the scene where Lisa runs into the attic as she dives behind the chest she rattles a bird cage, later when Ned faints you can see that the bird cage has disappeared.
Revealing mistake: When Bart is watching Rod and Todd walk over to Ned Flanders, you can see their reflections on Bart's telescope. Their reflections do not match their actual positions.
Other mistake: When Bart is looking at Doctor Hibbert on the rowing machine, all the pictures on the walls behind him don't have faces on 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