Continuity mistake: When everyone notices no food in the cooler, the cooler lid is raised, then it is down, then it is suddenly raised.
Continuity mistake: When everyone takes food out of the cooler, Bart has a bag of OREOs which magically becomes a bag of different cookies.
Continuity mistake: When the kids wash up on the island after the bus falls into the ocean, we can see they are totally dry. But they were just in water a minute ago, so they should be soaking wet.
Audio problem: When Milhouse is saying he's getting swimmer's ear, his mouth is out of sync whilst saying it.
Audio problem: When the bus is flying off the bridge and Otto says "Which way should I turn?" look closely at him when we can see his face during the line. We can see his mouth is out of sync when he's saying it.
Continuity mistake: When Homer and Karl are selecting a suit, just after Karl says none of the suits are to his liking, Karl's tie changes from green to red.
Continuity mistake: When Bart and Nelson first roll the orange and apple, we can see there is no-one sitting in front of Nelson. But a couple of shots earlier, we saw Milhouse sitting in front of Nelson.
Continuity mistake: On the bus, Otto rewinds his tape and there is a shot of the kids. In this shot, we can see the kids and nothing else. A couple of shots later, a food box has appeared out of nowhere.
Revealing mistake: At the U.N. meeting, Bart places his glasses down on the table to read out the Libyan exports. As he puts the glasses down, you can see they are unrealistically floating in the air.
Audio problem: When Homer says God is his favourite fictional character, his mouth is saying something different to what we hear.
Continuity mistake: When Homer has the Bill Of Rights, he ends up ripping several parts of it. The rips keep alternating between shots. (00:05:25)
Other mistake: When Marge takes Homer back inside, his car is seen blocking the traffic. But at least one side of the traffic is driving on the wrong side of the road. The drivers behind Homer's car are on the right side of the road. And the drivers behind Homer's car from the opposite direction are driving on the left side but facing the drivers behind Homer's car on the other side. Either way, one half of the traffic are driving on the wrong side of the road. (00:02:35)
Other mistake: When Homer returns home, Marge says his car is blocking the traffic. But there is some space on the road where his car isn't. The traffic could easily have driven through the empty space. (00:02:30)
Continuity mistake: Mr. Burns attempts to plan revenge on Springfield by placing The Town in a dome. However when Lenny tells Burns it has already been done, Mr. Burns tells the helicopters to stop placing the dome. In this shot, both Burns' helicopter and the helicopters placing the dome are the same height off the ground. But in the following shot, the helicopters are now 50 feet above Burns' helicopter. (00:18:55)
Continuity mistake: The X-rays of Homer's intestine change sides between shots when he is at the vet.
The Wizard of Evergreen Terrace - S10-E2
Continuity mistake: During the very last scene Homer is sitting on the sofa next to Bart watching the news. But in the last shot he's sitting in a separate chair next to the sofa.
Holidays of Future Passed - S23-E9
Factual error: When Lisa is trying to find Zia on the internet, the Google design shows Doctor Seuss because it is his birthday. Doctor Seuss' birthday is March 2nd. This takes place on December 24th.
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Audio problem: When Marge says "Save our families" at the beginning of her petition, her mouth doesn't move. (00:14:40)
Marge vs. Singles, Seniors, Childless Couples and Teens, and Gays - S15-E8
Continuity mistake: In the bathroom, Lisa can't stand the Roofi CD being played so she pulls the plug out of the plug socket to stop the radio playing. In the next shot, the plug has disappeared from the radio. (00:02:15)
Audio problem: When Homer says "I need change for a dollar. I also need a dollar", his mouth doesn't match what he's saying. (00:07:25)
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