Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I", when Hugo ties up Bart on the table in the attic, you can see that Bart's feet are tied up by pieces of rope. But when Dr Hibbert walks towards Hugo holding a picture frame, the rope is nowhere to be seen.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I", when the family are speaking to Dr Hibbert, there is a picture of Bart as a baby on the wall behind them. Later on in the scene, it disappears, and when Bart is by the staircase, it is back again.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I", when Homer and Marge return home in the pouring rain, Homer puts his hat on the hat stand. But when Bart is speaking to his mother, look at the hat stand and you can see the hat has gone.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I", when Bart is speaking to his mother after she has put down the phone, you can see Bart's arms are crossed, but when viewed from behind in the next shot, he now has his arms by his side.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I", when Bart, Lisa and Maggie are in the attic, Bart picks up a book and on The Front cover it shows a picture of Homer with the words "Homer, I Hardly Knew Me" by Homer Simpson. But when we see Bart with the book in the next shot, The Front cover is now completely clear.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I", when Lisa and Bart watch their father go to the fridge, you can see the spoons in their bowls are pointing to the left, but after a quick cut to Homer getting the fish out of the fridge, we cut back to Bart and Lisa and the spoons are now pointing to the right.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I", when the family are having their breakfast, you can there is a cup next to Marge's bowl, but when Homer gets up from his chair to go to the fridge, the cup is now near the edge of the table.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I", when Bart and Lisa come out of their bedrooms at the beginning, their doors are only partially open but in the next shot they are now fully open.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Homer3", when we hear Homer saying "I don't have much time" you can see Bart has a policeman next to him, but when we see a close-up of Bart in the next shot, the policeman has gone.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Attack of the 50 Foot Eyesores", when Homer puts the chain in the doughnut of the Land Lad Donuts logo, the position of the chain changes between shots.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Nightmare on Evergreen Terrace", when Bart is hit on the head by the Frisbee, you can see the Frisbee is further away from Bart, but a couple of shots later it is now by his feet.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Attack of the 50 Foot Eyesores", Homer enters the Lard Lad Donuts and you can see there is a straw holder on the counter in front of him. In the next shot, the straw holder has gone.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Attack of the 50 Foot Eyesores", when Lisa and Paul Anka perform their duet, you can see behind Anka there is a window and the bottom part of it is broken. But later on it is now completely intact and the two top windows are broken.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Attack of the 50 Foot Eyesores", when the cowboy logo on the Duff billboard comes to life, the position of the people next to the van changes between shots.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Attack of the 50 Foot Eyesores", when Homer answers the door and finds the Lard Lad statue in front of him you can see there is a door knocker on the door and a green doormat on the step. But when he answers the door a second time, the door knocker and doormat have gone.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Nightmare on Evergreen Terrace", when Bart says "You missed a spot" to Willie, the hose next to Bart changes position between shots.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Nightmare on Evergreen Terrace", when Bart and Lisa come into the kitchen to tell their parents about Martin's death, you can see next to Lisa's plate there is only a spoon but in the next shot a fork suddenly appears.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Nightmare on Evergreen Terrace", when Martin dies in the classroom you can see that in the desk next to Bart there is a boy student, but in the next shot he has changed to a girl.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Homer3", when Marge is eating the seashells with Patty and Selma, you can see the wall near the staircase is red in long shots, but in close-ups it changes to pink.
Tree House of Horror VI - S7-E6
Continuity mistake: In "Attack of the 50 Foot Eyesores", when the policeman shoots the football player who comes out of the Big and Tall Men's Shop, the shops change between shots.
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