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.
Continuity mistake: Throughout the trial, the twins keep switching places between shots. Note - one twin has a bow in her hair and the other twin doesn't.
Continuity mistake: When Bart says "No talking in the cage", both him and Milhouse are right next to each other. But two shots after Lisa says Milhouse is the only witness, Milhouse is a good 10 foot away from Bart without ever having moved the cage he was in.
Continuity mistake: At the start of the trial, Nelson is seen sitting in front of Martin and one of the twins. But in the shot after Lisa says Milhouse is the only witness, there is no sign of Nelson.
Continuity mistake: When everyone discovers Milhouse has eaten the food, Milhouse then says "You wouldn't dare hurt me. You forget, I have the glasses." After this line, Nelson takes off Milhouse's glasses. At this point, a rip is visible on the left side of Nelson's shirt. Milhouse then walks backwards and Nelson is seen re-entering the shot from behind Milhouse. Only now, the rip in Nelson's shirt is now suddenly on the right side of his shirt.
Continuity mistake: When everyone sees Milhouse after they find out the food has disappeared, Milhouse's arms are by his head. In the next shot, one of his arms is suddenly on his belly.
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 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.
Audio problem: When Homer is placing objects on the dining room table to start his website, he is whistling but his mouth isn't moving.
Continuity mistake: When Homer is at Moe's tavern talking about Marge, the level in his beer glass keeps changing even if he doesn't drink.
Continuity mistake: The offensive baseball cap that is in the Kwik-E-Mart changes from green to blue during the episode.
Continuity mistake: After Apu & Homer find Jasper in the freezer. Apu removes a note from his hand. Minutes later Dr. Nick walks in the door you see Jasper still holding the note then disappears again when Dr. Nick opens the freezer door.
Revealing mistake: In the scene where Marge is cutting Grampa's hair, his left cheek in the mirror's reflection turns blue.
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