Fat Man and Little Boy - S16-E5
Continuity mistake: When Homer goes to see Mr. Gladwell, in one shot, there is no plastic vomit, then a few shots later there is. (00:19:45)
Fat Man and Little Boy - S16-E5
Continuity mistake: In "Fat Man and Little Boy," Homer, while playing with Malibu Stacy, picks up Lisa and runs away from The Front door, which is behind him. In the next shot, however, Homer runs out of The Front door and into the street.
Continuity mistake: When Marge arrives home complaining that she is too tired to talk, there is an alarm clock on Homer's night table. When first shown it is a black electric clock, but when it is shown in the very next scene, it is an old orange one. Only a few seconds passed between these scenes, meaning there was no time for anyone to change it.
Homer And Ned's Hail Mary Pass - S16-E8
Continuity mistake: Homer is on The Front lawn when the bus of tourists turn up and Mario comes out. Homer gets mad and throws trash cans at Mario, who runs away and climbs up into the tree house which is at the side of the house, but it should be at the back.
Continuity mistake: The shaving cream on Chief Wiggum's face disappears when Bart tries to confess about the phony kidnapping.
Continuity mistake: Chief Wiggum's badge is shown to disappear under his fat in one scene, but in the following shot of him the badge is completely visible.
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.
There's Something About Marrying - S16-E10
Continuity mistake: Reverend Lovejoy is unable to cite which book in the Bible condemns homosexuality, but in "Homer the Heretic," he is able to recite, from memory, a completely random Bible verse.
On A Clear Day I Can't See My Sister - S16-E11
Continuity mistake: In Sprawl*Mart, the handle on the shopping cart disappears between the time Grandpa pulls the cart loose, and when you see him riding inside the cart.
On A Clear Day I Can't See My Sister - S16-E11
Continuity mistake: For "On a Clear Day, I Can't See My Sister": Throughout the episode, the backyard alternates between having a fence at the end and a forest at the end.
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)
Continuity mistake: The hospital band on Selma's right wrist keeps appearing and disappearing after they watch the menstration video. (00:03:00)
Continuity mistake: When Cletus arrives, to get his child back from Selma, we see Lisa wearing purple gloves. In the following shots, as she speaks to Selma, her hands are bare. (00:04:40)
Continuity mistake: After Selma gives Madam Wu the sack of ten thousand "happinesses" the sack instantly vanishes from off the table. (00:08:40)
Continuity mistake: The lock only appears on the door when Marge uses it. (00:14:45)
Continuity mistake: When the two chinese guards are dragging Budda Homer along, in an overhead shot we see a desk, with one filing cabinet behind it. In the next shot, the guards stop to rest, and now there are two. (00:17:25)
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.
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.
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