Ned 'N' Edna's Blend - S23-E21
Revealing mistake: When Marge is talking to Helen Lovejoy about Canapés at the party, Marge's mouth disappears for a single frame.
Continuity mistake: After Moe yells at Ralph, there's a woman in the background staring at Moe with an angry look on her face. She turns her head away from him after some seconds, but in the very next shot, she is looking at Moe with the same expression on her face.
Continuity mistake: When Milhouse snitches on Bart, Martin has grey hair and a black suit. In the very next shot he has his ordinary hair and is wearing a brown suit.
Continuity mistake: Jasper's beard is missing when everyone is singing "In-A-Gadda-Da-Vida" at church.
Springfield Connection - S6-E23
Revealing mistake: Homer's hand briefly turns transparent when he puts it on Marge's shoulder after he tells her to rip up the ticket.
Springfield Connection - S6-E23
Continuity mistake: While the Simpsons are eating breakfast, Lisa is eating what seems to be cereal from a bowl, but when she asks Marge if she needs to take a bullet for the mayor, she now has a plate in front of her with eggs and some other food.
Springfield Connection - S6-E23
Continuity mistake: The clothing of the women at the hair salon (Maude, Agnes, and Mrs. Krabappel) keeps changing color throughout the entire scene.
Revealing mistake: Mr. Burns' body is not seen through the window of his car when he tells Smithers to drive.
Homer vs. Patty and Selma - S6-E17
Revealing mistake: While the Simpsons are having dinner, the top portion of the chair Homer is sitting on disappears when he tilts the chair back.
Lisa on Ice - S6-E8
Revealing mistake: While Bart and Lisa are skating off the ice rink, the skin color of one of the people in the background during the riot keeps flashing yellow and brown.
Revealing mistake: When all the students are leaving Springfield Elementary after the fire alarm is pulled, the same students keep passing over and over again.
Revealing mistake: The people waiting in line for the game are extremely crude drawings. Some of them aren't even completely drawn, e.g, some are missing arms, legs and other body parts.
Lisa vs. Malibu Stacy - S5-E14
Continuity mistake: When the Simpsons are leaving the house to go to the mall. The aerial shot shows that they are leaving in Marge's red station wagon, but the very next shot of them in the car shows that they are in Homer's pink sedan. The shot of the station wagon leaving is probably a re-used shot from a previous episode.
Lisa vs. Malibu Stacy - S5-E14
Continuity mistake: When the Simpsons are about to leave the house to go to the mall, they're all wearing jackets, but when they're in the car just a few seconds later, none of them have their jackets on.
Revealing mistake: Apu's moustache disappears for some seconds after having his name tag removed.
Smoke on the Daughter - S19-E15
Revealing mistake: When Lisa turns on the light while dressed in her Angelica Button costume, her mouth disappears for a single frame.
Revealing mistake: While Lou is talking to Chief Wiggum about having his belt stuck to a street sign, Lou's mouth disappears for a single frame.
Four Regrettings and a Funeral - S25-E3
Continuity mistake: At church, while Marge is reminiscing about being pregnant with Bart, Kirk Van Houten is seen with grey hair and eyebrows. He has his ordinary blue hair and eyebrows in all other shots of him.
Revealing mistake: When Reverend Lovejoy arrives at church in the hot tub, there are two Carls right next to each other in the crowd.
A Test Before Trying - S24-E10
Continuity mistake: During the electricity rate hike announcement, Chief Wiggum is seen in the crowd incorrectly drawn with brown skin and black 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