Revealing mistake: When Skinner talks to Otto on the bus, the point of his hair is touching a pole. Look at the pole - Skinner's hair is going through it.
Character mistake: When Martin Prince supposedly represents Finland's culture for their recreation of the U.N at the Model U.N. Club Martin's outfit is not in fact a Finnish national costume. The outfit he is wearing actually resembles a traditional Sámi outfit. The Sámi people are the indigenous people living in Northern Europe. The specific style of Martin's outfit has characteristics that are more typical to the Sámi on the Swedish side of Sápmi. (00:02:15)
Continuity mistake: Bart, Lisa and Milhouse run away from the others and are stopped by a cliff. Milhouse then grabs onto a vine which was never there in previous shots. (00:19:00)
Continuity mistake: At the trial, Milhouse moves over to Lisa and Bart is in the middle of them. In the next shot, Bart has disappeared. (00:15:25)
Continuity mistake: Everyone discovers Milhouse ate the food so they walk up to him. The shot cuts and they are further away than they were in the previous shot. (00:13:50)
Continuity mistake: As soon as the fish bites Bart's butt and causes a rip in his shorts, the rip disappears almost instantly. (00:12:40)
Continuity mistake: The part of the bus that got a hole in causing it to sink changes position when Bart goes to get the cooler later. (00:07:10 - 00:12:20)
Continuity mistake: A fire is started when Milhouse's glasses are used by Nelson. But when Nelson hands Milhouse back the glasses in the next shot, the fire has disappeared. (00:11:40)
Continuity mistake: There are 10 kids stuck on the island. But after the kids have washed up on the island and it cuts to the wide shot and it shows them on the beach, there are only 6 kids. (00:07:20)
Continuity mistake: When the kids wash up on the island, Lisa, Wendell, Martin, Lewis and Sherri are on land and Bart, Milhouse, Ralph, Nelson and Terri are still in the water. In the next shot, Bart, Milhouse, Ralph, Nelson and Terri are on land with the others. (00:07:15)
Continuity mistake: The pens and pencils in the good butter change between shots when Homer begins his website. (00:04:55)
Continuity mistake: At the Model U.N. meeting, Bart finishes speaking and puts down his papers on the right hand side of his desk. Two shots later, the papers are on the middle of the desk. (00:03:10)
Continuity mistake: Whilst everyone is eating the boar, they are noticeably moving. But when it cuts the final wide shot, no-one is moving an inch.
Continuity mistake: When everyone discovers the monster is a boar, there is a Chippos packet on its tusk. But when the boar is shown licking the slime, the Chippos packet has disappeared without ever being touched.
Continuity mistake: When Milhouse swings across the vine, he lands on the ground and the vine isn't on the ground. Two shots later, the vine is suddenly on the ground.
Continuity mistake: Whilst running away from the others, Milhouse runs out of breath and falls over. In the shot where he is lands on the ground he has sweat on his face, but in the previous shot, no sweat was visible.
Other mistake: When Bart, Lisa and Milhouse run away from the others, Lisa steps right on a puddle but no splash or ripple is made.
Continuity mistake: Just before Homer meets Bill Gates, and during the meeting, the pens and pencils in the butter alternate between shots.
Continuity mistake: When Bart, Lisa and Milhouse first run away from the others and Nelson puts his fingers in the ash from the fire the night earlier, the twigs that remain in the fire disappear almost instantly.
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