Continuity mistake: When Bart and Ralph twist the key into the armed switch, the armed sticker is red and the off sticker is yellow. Then, during the press conference, the stickers switch colors. Then, when Mayor Quimby sits in the electric chair, they switch back.
Continuity mistake: When Tony Hawk and Homer compete against each other on the skateboards, Bart is on Tony's starting side. When Homer knocks Hawk off his skateboard, Bart is now on the side that Homer started on.
Waverly Hills 9-0-2-1-D'oh - S20-E19
Revealing mistake: In all the intro scenes from season 2 to season 20, episode 19, in the wideshot where Bart skateboards out of the school, if you look closely, part of the sky can be seen on the ground. (This mistake may only apply to the original format).
The Secret War of Lisa Simpson - S8-E25
Other mistake: When Lisa looks down from the platform before crossing the obstacle course, you can see her feet, but not the platform she stands on. (00:19:04)
Clown v. Board of Education - S34-E21
Continuity mistake: Fat Tony burns Krusty's tassel on his graduation cap. This causes Krusty to put it out and move it behind his head. In the next shot, it jumps back to the right side of the hat.
Factual error: When Hugh proposes to Lisa using the electronic signage, he spells the word "honor" using the American English spelling. Hugh should have used "honour" as this part of the show was set in England, and Hugh is from England.
Continuity mistake: This is a mistake for the introduction from seasons 2-20 (1991-2009). When Homer screams, he turns round. You see this in a wide shot. There are no boxes to the right of the door in the garage. However, two just appear out of thin air when he runs through the garage. (00:01:50)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: Lewis changes from black to yellow when Milhouse dares Bart to pull Santa's beard off. (00:14:10)
Continuity mistake: When Homer's Vegas wife shows him the video in front of Marge, it shows Homer kissing Ned. This didn't happen when she showed it in the Vegas episode.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Revealing mistake: After Homer brings Santa's Little Helper home, Homer and Marge hug, and if you look behind them, the background is upside down. There is a picture hanging upside down, and there is a lamp which seems to be hanging from the ceiling. Then in the next shot, the background is normal. (00:21:40)
Audio problem: After the donut delivery guy asks Carl why all the donuts are piling up, Carl responds with Lenny's voice.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: When you see a shot of the church from outside in the scene where the bee sharps sing there, look closely at the sign. It says 'Also: The Bee Sharps', only they don't name themselves that until later on in that episode.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: While having breakfast, all of the Simpsons' glasses of orange juice keep disappearing and reappearing throughout the scene. (00:05:35)
Continuity mistake: When Bart leaves the school, you can see that his skateboard is green and perfectly flat. But when he is skating through the crowd and past the people at the bus stop, the skateboard has an orange stripe down the middle and is raised at the rear.
Continuity mistake: Ms. Krabapple takes the cellular devices from the children in her class and puts them in a Laramie Cigarette box. She dumps the box into a desk drawer filled with frogs. A few seconds later there is a shot of the class from her point of view with all of their cellular devices on their desks. (00:03:00 - 00:08:15)
The Girl Who Slept Too Little - S17-E2
Continuity mistake: At the end of the episode where Homer is on the field talking to Buck the baseball player, the stadium is crowded. When Homer and Marge are leaving in their baseball golf car one second later, the stadium is empty. (00:20:40)
The Bonfire Of The Manatees - S17-E1
Continuity mistake: When Marge is in the car upset at Homer, the door to their house changes from open to closed then open again between shots.
Continuity mistake: When Maggie goes through the checkout at the beginning, Marge's trolley is grey and has a red handle. But in the next shot, when Maggie pops out of the bag, the trolley handle is turquoise. (00:00:30)
Continuity mistake: In the introduction, initially Maggie's seat is light purple. However, in the wider shot of her and Marge, the seat changes to a burgundy colour. (00:00:50)
The Bonfire Of The Manatees - S17-E1
Factual error: Alec Baldwin, as an expert on manatees, says that they are also called dugongs. Manatees are found in Atlantic coastal waters and in the Amazon and tributaries. The dugong is a distinct species found in the coastal waters of the Indian and southwest Pacific oceans.
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