Continuity mistake: The house is ripped from its foundations, but later on when it falls down the waterfall you can see the floor is completely intact.
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 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.
Strong Arms of the Ma - S14-E9
Audio problem: The speech does not match the lip movements from when Bart says, "dad, do you plan to get in shape?" until Lisa says, "Uh guys, mom just left the basement." (00:12:17)
Other mistake: When the Amish are building the tree house, the top of the tree is missing. It's just sky. In the next shot the top of the tree is back.
Strong Arms of the Ma - S14-E9
Audio problem: When the piano is playing Fur Elise, the keys do not move.
Strong Arms of the Ma - S14-E9
Audio problem: When Marge sprays the pepper spray at Ralph, the line she says after does not match her mouth.
Strong Arms of the Ma - S14-E9
Audio problem: When Homer says he'll eat twice as much, Bart says excellent, but that doesn't match his mouth.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Lisa goes to save Clara, she's wearing the same dress she took to the dance, but after Clara walks safely back to land, Lisa is wearing another outfit entirely, then changes back to her previous outfit in the very next shot, then back to her unknown outfit seconds later.
A Star is Born-Again - S14-E13
Audio problem: When Homer tells Ned "Flanders, I'm always interested in talking about free milk. And if there's cookies involved, so much the better", his mouth is not in sync with his voice.
Strong Arms of the Ma - S14-E9
Audio problem: When the woman who smashes the piano says "support the arts", her mouth is open, but it doesn't move.
Dude, Where's My Ranch? - S14-E18
Audio problem: When Homer and Bart go to destroy the beaver dam, Homer says "Oh, boy" without moving his mouth.
Dude, Where's My Ranch? - S14-E18
Audio problem: When Bart attempts to free Homer from the beavers, he says "I'll save you", but his mouth doesn't match what he's saying.
Dude, Where's My Ranch? - S14-E18
Audio problem: At the recording studio, when Homer sings the Frankenstein and Dr. No line, his mouth doesn't match what he is saying.
Bart vs. Lisa vs. the Third Grade - S14-E3
Audio problem: When the third graders get on the bus, Otto says "pukers in back", but his mouth is open and his lips don't move.
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.
The Dad Who Knew Too Little - S14-E8
Other mistake: When Bart flashes Lisa's laser at Principle Skinner's bottom, Chief Wiggum can still see it even when his car is in the way.
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