Continuity mistake: Milhouse's hair is blonde in the school bus' mirror reflection.
Continuity mistake: When Homer is shot at the hippie farm, he ends up with a flower in his head, stem first. But he put the flower in the gun barrel stem first, as well. From a shot at that close a range and that velocity, there's no way the flower could have turned around in mid-air.
Continuity mistake: When Red has finished the steak, he lies back and is the same position for Homer's small speech. However, as soon as Homer starts to say 'Wait, you're not breathing,' Red blinks when he is meant to be dead.
Continuity mistake: The name card display stand on Homer's desk disappears after Mr. Burns interrupts him.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: When Homer enters the bar, you briefly see that Lenny has dark green braces and a fawn coloured shirt. The next shot, they switch colours.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: At one point, Lisa and Bart are watching fireflies through the window. When Homer comes in, the fireflies are gone.
Sunday, Cruddy Sunday - S10-E12
Continuity mistake: When Homer gets the coupon book, look at the plant on the wall. It changes position between shots.
Sunday, Cruddy Sunday - S10-E12
Continuity mistake: The desk in the car repair shop behind Homer changes positions between shots.
Simpsons Bible Stories - S10-E18
Continuity mistake: When Bart is trying to wake up Homer, Maggie is seen with a blue pacifier. In the shot after the next, Maggie's pacifier is red.
Continuity mistake: When Ralph comes to see Lisa, she is wearing her turquoise slippers. However, after he leaves and she drops the book on the floor, her slippers have gone.
Continuity mistake: After Lisa wakes from her daydream, there's a boy behind her with blonde hair and a light purple shirt. After Ms. Hoover says "Then come back and finish the test", the boy's hair turns blue, and after it zooms in on Lisa's face, there's a boy with brown hair and a blue shirt behind her.
Monty Can't Buy Me Love - S10-E21
Continuity mistake: Ralph Wiggum is seen riding the train inside the mall, but is seen some seconds later amongst the crowd of people still waiting to enter the store.
Monty Can't Buy Me Love - S10-E21
Continuity mistake: Bart is next to Homer when Marge says "Where did you get that champagne?", but in the next shot, a clown is in the spot Bart was.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: During the song, Reverend Lovejoy at first has a blue sweater over his usual pink shirt, then he has a blue shirt, then he has his pink shirt without a sweater.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: When Dr. Hibbert says "Go ahead, girlfriend" at The Town hall, he is wearing a blue sweater, in the very next shot of everyone talking, he is wearing a pink sweater.
Thirty Minutes Over Tokyo - S10-E23
Continuity mistake: When Database is at The Java Server, he is using a teal computer, but when Snake comes in, he is using an orange computer, then he is using a teal computer again.
Marge Simpson in 'Screaming Yellow Honkers' - S10-E15
Continuity mistake: When Eddie the cop (as Curtis E. Bear) is being bludgeoned with 2x4's at traffic school, Krusty's nose is the same color as his skin instead of being red.
Wild Barts Can't Be Broken - S10-E11
Continuity mistake: When Wendell is among the kids seen inside the police van, his skin is a lot less pale than usual.
Continuity mistake: A huge fight begins in front of Mark Hamill's stage. Homer, Quimby, Hamill, Bart and Lisa escape the fight through an emergency exit right behind the people fighting. But in a shot of the five running out, the people fighting inside have disappeared.
Continuity mistake: When Homer has the Bill Of Rights, he ends up ripping several parts of it. The rips keep alternating between shots. (00:05:25)
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