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.
Large Marge - S14-E4
Factual error: In Luigi's, the lobsters in the tank are bright red. They are actually quite dark brown until they are boiled when they become red/pink.
Continuity mistake: When Homer shows his "incriminating photos," you can see that in them, he is bald. We know from several previous episodes that Homer had hair when Bart was a baby. He even has a bit of hair when Lisa is born.
Mr. Spritz Goes to Washington - S14-E14
Audio problem: At the end of the episode, when the guy who helped the Simpsons pass the bill says, "I just passed a bill in three hours. Quit complaining," his mouth movements don't match the words.
Brake My Wife, Please - S14-E20
Continuity mistake: As Hibbert handcuffs Bart to the radiator he uses the second bar to the right. The next shot it's moved to the next bar to the right.
Continuity mistake: After Kirk (Milhouse's dad) drives away from the stadium, Bart and Homer are walking along and you can see the Drink Duff sign right next to the edge of the fence. The next shot of Homer noticing the sign, the sign is further away from the edge of the fence and is smaller.
Scuse Me While I Miss the Sky - S14-E16
Other mistake: Bart and Lisa overload the nuclear power plant to create a city-wide blackout so everyone can see the meteor shower. All the lights in Springfield blow out. Yet when we see the Simpsons sitting on their lawn watching the shower, every single window in their house is yellow, as if every room has their lights on. It is the only house shown with power.
The Great Louse Detective - S14-E6
Continuity mistake: When we see the picture collage of Moe with the pickle jar the bottom picture is of them in front of the pyramids. When it pans around the pictures though, it turns into a picture of them on the beach.
Brake My Wife, Please - S14-E20
Continuity mistake: Whilst Bart is having breakfast he pours a lot of maple syrup onto his pancakes. When Marge walks into the kitchen to hurry him up the syrup on his pancakes has completely disappeared.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Lisa meets Clara, there is a close up of her necklace. The necklace is never there in any of the other shots that we see her. Her ring, as also seen in the close-up isn't visible either.
Treehouse of Horror XIII - S14-E1
Continuity mistake: The beers Homer puts under the hammock vanish when the hammock breaks, and Homer falls to the floor. (00:01:15)
The Great Louse Detective - S14-E6
Continuity mistake: When Bob pins Bart onto the wall in the final scene, his pajama top is stretched up so you can see his stomach. It then zooms in slightly when he looks at his watch and his stomach is covered.
Treehouse of Horror XIII - S14-E1
Continuity mistake: When everyone has been turned into animals, Police Cheif Wiggum, as a pig, takes off his tattered shorts and throws them into the fire. Later in the scene he's magically wearing them again. (00:19:40)
Scuse Me While I Miss the Sky - S14-E16
Audio problem: In Declan Desmond's film of Springfield Elementary shown at the end, Kearney and Dolph start beating Jimbo up. After Kearney says "Sellout," he says "Yuppie" in Dolph's voice. Then Dolph says "Soccer Mom" but in Kearney's voice.
Dude, Where's My Ranch? - S14-E18
Continuity mistake: When Homer is playing the song on the piano, one of the photo frames on the top of it keeps changing from square to oval.
Bart vs. Lisa vs. the Third Grade - S14-E3
Continuity mistake: When we first see Willie standing by the Black Wall of field trips, the latest entry is at Willie's eye level. But when the angle changes, there are a lot more names on the wall, making the last entry appear just by Willie's chest.
Dude, Where's My Ranch? - S14-E18
Audio problem: When Bart gets the beavers to knock down the tree so that Clara can walk across, she gets onto it and starts walking gently. But when she walks gently, it sounds like she's walking quickly across the trunk.
Treehouse of Horror XIII - S14-E1
Continuity mistake: The people standing to the left of the rock, as the Comic Book Guy (as a faun) walks onto it, changes. In the first shot the police officers and Raplh stand there, in the second shot it's a panda. (00:19:25)
Treehouse of Horror XIII - S14-E1
Continuity mistake: When Homer starts to strangle his clone, the clone throws the boxes it was carrying, to the floor. In a following shot the boxes have vanished. (00:04:20)
Special Edna (a.k.a. Love and Marking) - S14-E7
Deliberate mistake: When Bart and Edna are watching "Holes" in the IMAX theater, Edna sighs and pulls out a locket which we can see the back of. After opening it up to reveal pictures of her and Seymour, we find out its actually a triptych when she opens up another image of Seymour's mother. From the way she unfolds this extra picture, Seymour's mother would have had to be facing outwards, but in the previous shot the back of the locket was blank.
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