Continuity mistake: When Homer goes to catch Maggie (after flying out of the car) he jumps over two cars in front of him and then falls over the second one and there is no sign of any cars in front of him. However in the shot before he climbs over the cars the aerial shot of Maggie flying in the air, all the cars on the bridge are bumper to bumper with no spaces in between them.
Continuity mistake: After the slinky leaves Moe's hands, and goes out of Maggie's room, we see that Maggie's toy phone is right next to the door way, then when the camera goes towards Moe, and Maggie, then we see the toy phone next to Moe and Maggie.
Continuity mistake: When Moe is rocking Maggie, the little image of the flower that is on the rocking chair is purple. Then when Moe gets up, the flower is white.
Continuity mistake: When Maggie is opening her presents, the biggest present is pink. Then after Patty and Selma walk away, the biggest present is blue.
Continuity mistake: Moe's back pockets, the pockets on his bum, change position/disappear between shots - before the Italian-American-Mexican stand-off.
Continuity mistake: In the scene where Maggie swallow' Moe's penny, she first takes out her pacifier to eat it, but in the next shot it's in her mouth again and in the next, she's putting it back in her mouth.
Treehouse of Horror XIV - S15-E1
Continuity mistake: When the younger Professor Frink is receiving and wearing his Nobel Prize, his father goes nuts and starts stealing people's brains. The younger Frink figures out that kicking the elder Frink in the crotch will stop him. When he does, and the elder Frink falls off the stage, he is wearing the Nobel Prize, not the younger. (00:15:00)
Treehouse of Horror XIV - S15-E1
Continuity mistake: The piles of sweets and candy that Bart and Lisa have at the start vanish in the wide shots when Homer arrives.
Treehouse of Horror XIV - S15-E1
Continuity mistake: After Homer tries to stab himself with the banana, he drops it. But when Nelson's clothes disappear, the banana has vanished.
My Mother the Carjacker - S15-E2
Continuity mistake: When Homer is looking for a message to stop Grandma Simpson and the jail bus on the electric sign he has Bart with him. Then Bart is not on the bus with Homer and Grandma, but he is back at the end of the episode.
My Mother the Carjacker - S15-E2
Other mistake: In the scene where the prisoners are singing along with Mona, two inmates have the same Identity number.
My Mother the Carjacker - S15-E2
Continuity mistake: At the end of the episode when Homer is looking for another message from his mom to find out if she's really alive, Marge and the kids enter the kitchen, Marge says that it's 2 in the morning. But the clock on the wall shows that it's 9 pm.
The President Wore Pearls - S15-E3
Continuity mistake: When Lisa goes into Principle Skinner's office to resign, there is a mug and some papers on the desk. When she wants to use the microphone, the desk is clear.
The President Wore Pearls - S15-E3
Continuity mistake: At the end of the episode Lisa gets on the school bus and in the back of the bus there is an emergency door with a small window in it. The following shot she starts singing out the back of the bus but the window has disappeared.
The Fat and the Furriest - S15-E5
Factual error: Homer creates a giant sugar ball by making a normal sized cotton candy on a paper cone, and then coating it with liquid caramel. The cotton candy holds its shape and Homer continues to expand it with more cotton candy and caramel. However, cotton candy dissolves very quickly and tears apart easily. Between the weight and moisture content of the caramel, the original cotton candy would have immediately melted and/or collapsed.
The Fat and the Furriest - S15-E5
Continuity mistake: When Homer realises that the bear was only agressive because of the electrical tag, they share a bear hug. The back of Homer's shirt is torn to tatters, and his back is bleeding. Immediately thereafter, the back of Homer's shirt is completely intact.
Continuity mistake: After Homer pushes in front of Lisa in the queue for the bathroom, she loses the toothbrush she was holding in her left hand. (00:01:15)
Continuity mistake: When we first see the medicine cabinet in the Simpson's bathroom the hinges are on the left. When Homer pokes it with the wire it opens as if the hinges are on the other side. The last time we see it, when Lisa rescues Maggie, the door is missing altogether. (00:01:25)
Continuity mistake: After he takes a puppy from Bart, Snake's car appears from nowhere. (00:04:15)
Continuity mistake: When Krusty ends up at his old neighbourhood, the street changes between shots. E.g. the "LLBeanie" sign appears above the door of the 2nd shop and the suit of the man reading the newspaper changes from grey to blue. (00:05:25)
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