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.
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.
Home Away From Homer - S16-E20
Continuity mistake: When Homer rings the doorbell of the Flanders' former house to visit the new neighbour, it moves downwards on the door frame. In the first shot it lines up with the gap between the lock and the doorknob, but in the next shot it is beside the doorknob, and in other shots in the episode the doorbell isn't even there. Also, the glass panels on both sidelights line up with the door differently between shots.
Home Away From Homer - S16-E20
Continuity mistake: As the Simpsons are in the cinema watching "Kosovo Autumn" you can see there is a seat next to Homer to the right of screen. When Homer starts complaining about the film but cannot leave because he is stuck in his seat, the shot changes and we see him from behind however the seat that was next to him has disappeared.
Home Away From Homer - S16-E20
Continuity mistake: When Coach is cutting down trees he tells Homer that he borrowed some petrol (or 'gas' in America) from his car, and the shot goes to his car. However when Homer runs indoors the car has vanished.
Home Away From Homer - S16-E20
Continuity mistake: For "Home Away From Homer": Bart looks out his bedroom window and sees the college girls doing sexual actions in the Flanders' spare bedroom. But, there is never a window in Bart's room that could possibly face the Flanders' house. [Bart's window in many episodes does face Flander's house but in other episodes like "Bart's Friend Falls in Love" and "Bart the Mother" it faces the treehouse which is the backyard of the house.]
Home Away From Homer - S16-E20
Continuity mistake: Ned's front door before he and his family leaves opens on the left side (when looking at it from outside), but after the "Coach" has moved in, it opens on the opposite side.
Home Away From Homer - S16-E20
Continuity mistake: When Homer tries to leave his seat in the cinema and complains about eating the apple, the shot shows his body fat has wedged him in the seat. However we can see from all the shots before this that the fat was never wedged in like it was when he was trying to leave.
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