Continuity mistake: At the end when Nelson's goons are holding on to Nelson, they both have brown skin. But in the next shot, one of them goes back to having yellow skin.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: When Homer brings Santa's Little Helper home, a single frame of Maggie falling off Marge's lap is misplaced.
Continuity mistake: When Agnes meets Bart and his friend, it cuts to Skinner, then to Bart's group and quickly back to Skinner. When it goes to Bart's group (before Skinner) Lewis is yellow like the rest, in all other scenes he is black.
Continuity mistake: When the robbery happens, Homer steps on the robber's feet, and we can tell he has large shoes. When they show video of the robbery on the news, the robber has regular shoes. During the hearing, they watch the video again. His shoes are back to long again.
Continuity mistake: When Sherri and Terri raise their hands and say "like us Mrs. Krabbapple" they raise their hands over their heads. Camera cuts and their hands are a lot lower. (00:04:20)
Continuity mistake: When the teacher is looking out of the window, Bart has his paper in front of him on the desk. The paper disappears in the next shot, but reappears when Bart takes Martin's paper off the table and puts it on his desk. (00:06:10)
Continuity mistake: Millhouse's hair color changes from when we first see him to when Bart comes back to the school yard.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Audio problem: When Lisa and Maggie are touching Bart's surgically removed tattoo, he says "Ow", but look at the way he says it. His mouth moves when he says "O" but doesn't move when he says "w". (00:07:50)
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