Continuity mistake: In the first shot of Selma on the hospital bed, there's nothing behind Patty. However, when Marge starts to speak, we suddenly see two bags of drip mounted on a dripstand behind her. (00:01:55)
Treehouse of Horror XV - S16-E1
Continuity mistake: Ned hammers in the For Sale sign; a few shots later, when Homer comes, it is no longer there. (00:03:40)
Home Away From Homer - S16-E20
Continuity mistake: When Homer meets Coach for the first time (and maybe another point in the episode), the position of Ned's house's window frames to the side of the door change between shots.
Continuity mistake: When Bart and Tab Spangler arrive at the Simpson house, Mr. Spangler points out the belt he is wearing to Bart. But as he leaves Bart and walks to his car, he is suddenly not wearing a belt at all.
Treehouse of Horror XV - S16-E1
Continuity mistake: When Maggie crawls out of the stroller and into the capsule, the stroller has no harness, but when Marge sees the empty stroller, there is a harness.
Home Away From Homer - S16-E20
Continuity mistake: We see Coach cutting down trees in Flanders' former driveway. However there had never been any trees in Flanders' driveway.
Revealing mistake: In the opening sequence's parody of the series where Bart becomes fat and comes out from school on his skateboard, he theoretically should go down the stairs, instead his silhouette suddenly climbs up on the wall next to him, revealing a mistake in the post-production's animation. (00:06:05)
Continuity mistake: When Cameron is being booed, Lenny's five o'clock shadow is missing, it returns in the next shot.
Continuity mistake: After Lisa's final performance, Bernice Hibbert (sitting next to Dr. Hibbert) has light brown hair instead of black/dark brown.
Continuity mistake: After Lisa's last performance, Carl and Lenny are seen with grey hair.
Continuity mistake: After Lisa finishes singing her song during the audition, there are several coloring mistakes in the shot of the audience clapping. Agnes Skinner's face is ghost white, but her hands are yellow. Mayor Quimby's suit is lavender instead of violet/blue, and his hair is light brown instead of medium brown. Helen Lovejoy has blonde hair instead of grey, and is wearing a purple shirt instead of pink sweater over blue shirt, and Reverend Lovejoy has a green shirt instead of pink, and has brown hair instead of black.
Don't Fear The Roofer - S16-E16
Audio problem: When Marge says "You're drooling on my goodwill pile", her mouth doesn't match her voice.
Continuity mistake: When Bart goes up to his treehouse to write the kidnap letter, he throws his Murder 4 Life jumper out the treehouse entrance. Later, when Lisa finds the jumper, it is now on a tree branch as if he threw it out of one of the treehouse windows.
Audio problem: When Homer says "Burn the truth" after burning his pants, his mouth doesn't match what he is saying.
Don't Fear The Roofer - S16-E16
Revealing mistake: When Homer sits on Lenny's cake in Moe's bar, some of the frosting appears to stay in mid air, and when the frosting is on the wall, it doesn't slide to the ground like frosting would.
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