Large Marge - S14-E4
Continuity mistake: In some shots, the incorrectly-colored lobsters have their claws taped shut, and in others they don't. It's completely random.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: Carla's "Carla" ring is only on her finger in the closeup.
Brake My Wife, Please - S14-E20
Continuity mistake: When Hibbert handcuffs Bart to the radiator, for one brief second, his cast and bandages disappear. They return in the next shot.
Continuity mistake: On the trip back from the gardens, Homer rear ends the car in front of him on the bridge which sends Maggie flying out of the car. In a long shot of the bridge whilst Maggie is in the air you can see the car has changed to an orange color instead of the usual light purple color. The two cars in front of them also change during shot. The one in front of the simpsons changes from a normal red mid sized car to a blue van, whilst the car in front of that one changes from being a green car to a blue one during the aerial shot of Maggie.
Continuity mistake: When Homer bangs on the screen in the testing booth, the little sign on the top left of the glass that was there earlier is no longer there.
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.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Luke jumps off of the horse to save the rattlesnake egg, the horse changes from being beside Luke to beside Lisa between shots.
How I Spent My Strummer Vacation - S14-E2
Continuity mistake: When everyone is getting guitars, Homer is among the people who are waving their hands to get one but in the scene before it, when they are in the cabin, Homer already had one.
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.
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.
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.
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