Continuity mistake: After Marge has bitten the candle down to size, when she wipes Bart's face her left earring vanishes, then it reappears. (00:03:35)
Continuity mistake: While Marge and Homer are standing by their front door when everyone leaves the house Marge is wearing earrings, but when it cuts to the closeup both of Marge's earrings have vanished. (00:08:10)
Continuity mistake: In the beginning, the family is eating in front of the T.V. When Marge is complaining about getting the food all over the floor, she drops her meatball on the floor, and it leaves a trail of sauce on the rug. In the bird's eye view of the room, the sauce has disappeared until the shot changes: then it reappears.
Continuity mistake: Marge said to Bart she would make Butterscotch chicken for him, but in the Season 2 episode "Blood Feud" Marge says Bart's allergic to butterscotch.
Continuity mistake: When Marge opens the dishwasher and tells Lisa to reattach the toilet seat, there's a red dish rack on the counter over the dishwasher, but in the previous and following shots there's a filled casserole dish over the dishwasher, not a dish drying rack.
Continuity mistake: After Marge bites the candle down to a smaller size, the candle turns back to its original size for a frame.
Lisa's Date with Density - S8-E7
Continuity mistake: When Jimbo and Co are 'coleslawing' Skinners house, he wakes up when coleslaw hits his window. When the shot moves to outside, there isn't any coleslaw on any of the windows.
Lisa's Date with Density - S8-E7
Continuity mistake: Whilst Chalmers notices the Honda symbol missing from his car, there are four holes in the corners of the leftover symbol. There is a screw in one of the holes indicating the symbol would have holes in its corners to hold it down. Later when Skinner finds the Honda symbol in Nelson's locker you can see there are no holes in the symbol.
Lisa's Date with Density - S8-E7
Continuity mistake: The hole in Nelson's locker increases in size.
Lisa's Date with Density - S8-E7
Continuity mistake: As Homer is walking out of the Kwik-E-Mart, after Apu refuses him the donut, he has nothing in his hands. In the next shot from outside the store we see him carrying a small paper bag.
Lisa's Date with Density - S8-E7
Continuity mistake: In Lisa's music class, there is a wide shot of the entire class. Üter sits next to Milhouse Van Houten in this shot. However, in the next shot, it's Ralph Wiggum. In a following shot of the entire class, it's Üter again. They both replace each other in the same seat.
Other mistake: The doctor in the insane asylum shows a video that shows a child Ned Flanders from 30 years ago. Ned is 60.
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.
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