Continuity mistake: Ned's clothes are cut and torn in the huricane, but the next day, they are somehow clean and intact. He can't have gone home and changed, otherwise he would have seen everyone repairing his house.
Continuity mistake: When Ned stops to snap at Lisa he's already yelled at Marge and Bart. Yet in the background you can see Marge among the secondary characters.
El Viaje Misterioso de Nuestro Homer (a.k.a. The Mysterious Voyage of Our Homer) - S8-E9
Continuity mistake: When Homer is freaking out and starting to hallucinate after eating a few peppers, Jasper is behind a tent stall when Homer is running away from Ned Flanders, but just seconds later when Homer falls to the floor, Jasper is in front of Homer. (00:08:05)
The Springfield Files - S8-E10
Continuity mistake: After the scene with the T-shirts, when the alien arives, Marge's "Homer is a dope" shirt disappears and she has her normal dress on.
The Springfield Files - S8-E10
Continuity mistake: At the kitchen table, when Homer talks about getting mocked on his own birthday, they're eating breakfast. But when Marge, Lisa, Bart and Maggie all go to pet Santa's Little Helper, the breakfast has vanished.
The Springfield Files - S8-E10
Continuity mistake: When the 'alien' is seen on the news, it is shown on the film Bart made coming out of the trees, but earlier on, when the alien came out of the woods, Bart is seen not holding the video camera.
The Twisted World of Marge Simpson - S8-E11
Continuity mistake: At the fair, Helen Lovejoy picks up a pita and bites a corner off it. There are a few angle changes and when it goes back to her and you can see her pita looks untouched. It's unlikely she just picked up another one or finished a whole one in that time.
Continuity mistake: When Mr Burns and Homer first enter the cabin, you can see the door opens with a door knob which is on the right hand side (looking from the outside). Later, after the avalanche, the door seems to open a different way, the knob has been replaced by a handle and it's on the other side.
Simpsoncalifragilisticexpiala(Annoyed Grunt)cious - S8-E13
Continuity mistake: During the song "Its the American Way" Snake is robbing Hans Moleman during Chief Wiggum singing and Snake's hair is blue. His hair has always been a brown-red color. In the very next scene to confirm its a mistake you see him in the park saying "Yo Sherry Bobbins" and his hair is back to its brown-red color.
Simpsoncalifragilisticexpiala(Annoyed Grunt)cious - S8-E13
Continuity mistake: When the family are watching Krusty Komedy Klassics, at the beginning of the show, they all have grey tables, with their dinner. But when Bart asks for milk, Marge gets up to get it and her table has disappeared. When she comes back the table has re-appeared.
Simpsoncalifragilisticexpiala(Annoyed Grunt)cious - S8-E13
Continuity mistake: When Bart is lying on his bed whipping cupcakes at the wall, there are already 2 on the wall but after he whips the 3rd, there are still only 2 cupcakes on the wall.
The Itchy & Scratchy & Poochie Show - S8-E14
Continuity mistake: During the last taping of Homer's Poochie character, June Bellamy is standing beside Homer, and she's wearing a watch on her left wrist, but her watch vanishes in some shots. (00:19:40)
Continuity mistake: After John shows up in his car to take the Simpson family for a drive, Marge has her purse strap hanging off her left shoulder when she asks Homer to at least say hello to John. In the next shot, as she tells Homer that he liked John that morning, note Marge's purse strap is missing from her shoulder, but the purse is still there just hanging in midair under her arm. The strap reappears in its proper place in the next shot. (00:07:50)
Continuity mistake: John is wearing Homer's old "Pin-pals" bowling shirt when the Simpsons first meet him, but only after we see the back of the shirt does the name "Homer" appear over John's breast-pocket; clearly there was nothing there during their entire previous conversation. And even if this is a deliberate "mistake" for comic purposes, in 7th season episode"Team Homer", the very same bowling shirt is ripped to shreds when Homer is being mauled by Mr.Burns' dogs at the very end.
Brother From Another Series - S8-E16
Continuity mistake: In the scene where Sideshow Bob and his brother Cecil are arrested and sits in the the back of the police car, Cecil is missing when Sideshow Bob is talking to the people outside the car though his window. They both entered the car and they can both be seen when the car leaves.
Brother From Another Series - S8-E16
Continuity mistake: When in the dam Bob stops the motors from spinning. Next shot shows the blades spinning again, but when the camera cuts they are stopped again.
Brother From Another Series - S8-E16
Continuity mistake: Sideshow Bob and Cecil's glasses keep switching from wine glasses to champagne glasses while they are having dinner.
Brother From Another Series - S8-E16
Continuity mistake: In the shot where Homer yells, "Marge, I'm going to look for the kids," their door is shut. After Homer sees the wave and runs back inside, their door is open all of a sudden.
Brother From Another Series - S8-E16
Continuity mistake: Reverend Lovejoy is standing behind Sideshow Bob during his speech, but in one shot, he is standing with the protesters, then back behind Bob.
Brother From Another Series - S8-E16
Continuity mistake: Ruth Powers' hair is red in one of the shots of the protesters. Her hair is brown in other shots of her.
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