Continuity mistake: When the Flanders and Simpsons first meet at the golf course, Flanders is wearing his usual long-sleeved green sweater over his shirt. After Homer says to him, "The fruit of my loins can beat the fruit of your loins any day of the week", the color of Flanders' sleeves is missing, making it look as if he's wearing a sleeveless pullover.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I": After the kids have found Hugo in the attic, when Marge and Homer return home, both front door knobs (inside and outside) do not have backplates, but once Hugo escapes both door knobs have backplates. The two backplates vanish and reappear repeatedly in following shots. It's funny because when they leave to search for Hugo, Homer shuts the door with no backplates, but then Bart uses a key in the backplate to lock The Front door.
Revealing mistake: During the first ten minutes when the twins are explaining to Bart what incompetence means, one of the twins' body disappears, showing a floating head and hair. (00:06:30)
Gump Roast - S13-E17
Continuity mistake: When Kang and Kudos are electrifying Krusty; when they stop his clothes are fine for one split second, then the clothes are destroyed.
Continuity mistake: When Homer has his car towed from the bank, it is hooked up at the rear. When they arrive at the impound lot, it is hooked up at The Front.
Springfield Connection - S6-E23
Continuity mistake: When Marge is lying on the sofa reading her book the red lamp behind her is first seen to be fully red.In a following close up shot it has an orange rim on the bottom of the shade.
Continuity mistake: After Marge is looking at the matchbox from the Maison Derriere it just disappears when she sits on the sofa.
Three Men and a Comic Book - S2-E21
Continuity mistake: When Martin is tied to the chair near the end of the episode, the number of ropes tied to him change from four, then to three, and then back to four.
Continuity mistake: Bart's 1st grade drawing of cat on the fridge changes across the episode, especially its ears and whiskers. (00:04:50)
Audio problem: Both Lenny and Carl's voices are wrong. At one point Carl's voice is higher pitched, and Lenny keeps speaking like Moe, or like a voice we haven't heard before.
Continuity mistake: Just before Apu has a flashback of Helen Lovejoy and Moe interacting in the church, Reverend Lovejoy is in his black shirt and collar. after the flashback he is in his casual pink shirt and blue tie.
Guess Who's Coming to Criticize Dinner - S11-E3
Continuity mistake: When all the people who are plotting to murder Homer are talking about the reviews Homer had given them, Akira says, "So why did you put yours in the window?" and you see the review. At the end of that scene, when they are all laughing, you see the building they are in, and it has nothing in the window.
The Great Louse Detective - S14-E6
Continuity mistake: When Homer and Sideshow Bob are chasing the mechanic on stilts, the mechanic tries to get away, and his cape falls off while he is being chased. In the next shot, we see a close-up of the mechanic, and you can see his red cape is back on again. Then in the next shot, we see Homer and Bob chasing him, and his cape is off.
Continuity mistake: Homer's two hairs over his head are dishevelled when the family arrive at Itchy and Scratchy land due to whatever has happened on the detour - however, it suddenly changes to being like he normally has it in the last frame that shows the family in the car, before the car park is shown.
Continuity mistake: When Bart visits the kid's train ride, the first shot of it shows that it starts with a big curve before the tunnel. When he goes on it the track is straight before the tunnel.
Continuity mistake: In the old main title sequence, when Homer gets out of his car, the door inside the garage is red, but when he is screaming and running towards it, it's now brown. (00:01:40)
Continuity mistake: The right handle plate on Homer's gun is fastened with two screws throughout the entire episode. But in the scene where he promises Marge to get rid of the gun and they hug in the kitchen, the gun is seen lying on the table with only one screw in the handle.
Continuity mistake: When Bart crashes at the social club, his skateboard changes position between shots. (00:05:30)
Continuity mistake: When Bart hands Ms.Krabbappel his final test, there are some shots going back and forth between their faces. During the first shot looking at Ms.Krabbappel, you can see a window behind her, and outside the window, there is no snow, even though there was a whole lot of it yesterday. During the next shot, the snow IS there. As the camera goes back and forth, the snow disappears and reappears.
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