Continuity mistake: When Tony Hawk and Homer compete against each other on the skateboards, Bart is on Tony's starting side. When Homer knocks Hawk off his skateboard, Bart is now on the side that Homer started on.
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: 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.
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.
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)
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.
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)
Continuity mistake: At the birthday party Maggie is playing in the sandbox with one of Apu's kids. She and Apu's son both have pink with green polka-dots party hats on. After she is taken out of the sandbox by Moe, Homer takes her and she keeps squirming out of his arms. Look on her head and you'll see that her party hat has disappeared, and never comes back.
Scuse Me While I Miss the Sky - S14-E16
Continuity mistake: When Skinner opens the door to the room Lisa is in, there is a red book with white rings around it behind the door, it is easily the most noticeable book on the shelf. When the shot cuts back, the book is suddenly blue.
Continuity mistake: When Grandpa goes nuts outside the house he knocks over 2 bins and spills rubbish on the pavement, in the next shot the bins and the rubbish are gone.
Brake My Wife, Please - S14-E20
Continuity mistake: Whilst Moe is talking to himself about going back to barber college the door to his bar is wide open. When the shot changes to him when he says "Who the hell am I talking to?" the door has suddenly closed. There was not enough time for it to close between shots.
Large Marge - S14-E4
Continuity mistake: After Homer paints "El Homo" on the wall, he paints over it so that none of the letters are visible. In the next shot a couple of the letters are visible, and are only struck out with one line.
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