Continuity mistake: There is a latch on the crate when Bart opens it and Laddie appears, but when Laddie jumps out of the crate, the latch has gone.
Continuity mistake: When Bart opens the door and finds the crate containing Laddie, there is nothing on the doorstep but in the next shot a green mat appears.
Continuity mistake: When Lisa comes into Bart's bedroom, the number of balls in the bottom tray of the bagatelle game increase between shots.
Continuity mistake: When Bart sees "The Covet House" order in the catalogue he has picked up from the trash can, he is reading it with both pages open, but when we see him in the next shot, he is reading the catalogue with the back pages folded under.
Continuity mistake: When Bart is at the Card Shop, he picks up the magazine "Zoidzilla" and put on the top of the pile he is holding. But when he takes the pile to the cash desk, The Front cover of the magazine is now coloured green.
Continuity mistake: When Marge discovers a letter for "Santos L. Halper", Bart has nothing in front of him on the table. In the next shot, a knife, fork, bowl and glass have appeared.
Continuity mistake: When we see Bart holding the post, he is initially holding it with one hand, but when we see a close-up of the post in the next shot, he is holding it with both hands.
Continuity mistake: When Marge finds Lisa's German verb wheel in the post during the breakfast scene at the start of the episode, you can see Lisa has nothing in front of her. In the next shot, a bowl and a glass have appeared.
Tree House of Horror VII - S8-E1
Continuity mistake: In "Citizen Kang", when the alien whips Marge's behind, you can see in the background there is a tree that changes to a crane in the next shot.
Tree House of Horror VII - S8-E1
Continuity mistake: In "Citizen Kang", when Homer pulls off the masks off the fake Clinton and Dole at the White House, the two transform into aliens and you can see Homer is between them. In the next shot, Homer is missing, and in the shot after that, he is back again.
Tree House of Horror VII - S8-E1
Continuity mistake: In "Citizen Kang", when Homer tries to save Clinton and Dole in the spaceship, Homer is standing behind a control panel and you can see there is nothing on left of it, but in the next a large lever suddenly appears.
Tree House of Horror VII - S8-E1
Continuity mistake: In Citizen Kang, when Kang and Kodos (as Clinton and Dole) are speaking to the man from the Democratic National Committee, you can see the building in front of them has a plant outside and there are shades on the windows. But when Homer appears in the next shot, the plant and shades have gone.
Tree House of Horror VII - S8-E1
Continuity mistake: In "Citizen Kang", when we see the family eating breakfast at the table, you can see that Bart has a bowl in front of him. But when Homer comes into the kitchen, there is now a glass by the bowl, and in the next shot the glass has gone again.
Tree House of Horror VII - S8-E1
Continuity mistake: In "Citizen Kang", when Kang and Kodos are transformed into Clinton and Dole, Homer is standing in front of the control panel and you can see in front of him there are several buttons, but in the next shot there is now only a green and red button in front of him.
Tree House of Horror VII - S8-E1
Continuity mistake: In "Citizen Kang", when Bill Clinton and Bob Dole are in the suspended animation tubes in the aliens' UFO, you can see that Clinton is facing left in one shot, but a few seconds later he is now facing right.
Tree House of Horror VII - S8-E1
Continuity mistake: In "Citizen Kang", when Homer is fishing, you can see behind him on his boat there are a brown box and a rolled up mat, which is standing up. But when we see a view of Homer's boat from the UFO, the mat is now lying flat on the back of the boat and the box is now coloured red.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Genesis Tub", when Lisa comes to the table to eat her toast, there is a glass next to her that changes position between shots.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Genesis Tub", when Lisa takes the bowl of cola to the microscope on her dressing room table, you can see a brush near the edge of the table, but in the next shot the brush is behind the microscope.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Genesis Tub", when Bart comes into Lisa's bedroom with a balloon behind his ear, he goes to see Lisa. In the next shot, Bart is much near the door, and in the shot after that, he is near Lisa again.
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I", when Homer puts a blanket on the floor for Hugo to rest his head on, you can see Homer is standing by Hugo. In the next shot, Homer is standing by the blanket.
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