Tree House of Horror XII - S13-E1
Continuity mistake: In "House of Whacks", when Homer attacks the tank, he puts the axe in the right hand side of the tank, but in the next shot the axe is now in the middle of it.
Tree House of Horror XII - S13-E1
Continuity mistake: In "House of Whacks", when the tools are attacking Homer, you can see one of the tools puts shaving foam on his face. But when he is walking down the stairs, the foam has gone.
Tree House of Horror XII - S13-E1
Continuity mistake: In "House of Whacks", when Homer is sitting on the settee, you can see his beer glass is empty, even though a few seconds ago it was nearly full.
Tree House of Horror XII - S13-E1
Continuity mistake: In "House of Whacks", when the dishes are cleaned, you can see by Marge's plate there is a spoon and a fork. In the next shot, there is now only a spoon, which disappears in the next shot.
Tree House of Horror XII - S13-E1
Continuity mistake: In "House of Whacks", when Marge has finished eating her meal, you can see a spoon on her plate. But when she is seen on the camera, the spoon has gone.
Tree House of Horror XII - S13-E1
Continuity mistake: In "House of Whacks", when Marge opens the door to the robotic salesman, you can see there is a green mat under the door. But when the salesman puts his foot between the door, the mat is missing, and in next shot the mat has re-appeared.
Tree House of Horror XII - S13-E1
Continuity mistake: In "Hex and the City", when the leprechaun knocks Marge's glass over on the table when she is eating her pancakes, the glass changes position between shots.
Tree House of Horror XII - S13-E1
Continuity mistake: In "Hex and the City", when Homer puts his spade in the ground when he is digging a hole with Bart, the spade keeps disappearing and re-appearing between shots.
Tree House of Horror XII - S13-E1
Continuity mistake: In "Hex and the City", when Lenny and Carl are crushed by the helicopter at the tavern, the liquid behind Lenny is white but changes to brown in the next shot.
Tree House of Horror XII - S13-E1
Continuity mistake: In "Hex and the City", when Homer, Bart, Lisa and Maggie are eating their breakfast at the table, they see Marge with a blue beard and Homer spits some food on the table. In the next shot, the food has gone, and when Homer goes to strangle Bart, it is back again.
Tree House of Horror XII - S13-E1
Continuity mistake: In "Hex and the City", when the Fortune Teller is speaking to Homer in her office, you can see the crystal ball is in front of her but in the next shot it has moved to the edge of the table.
Tree House of Horror XII - S13-E1
Continuity mistake: In "Hex and the City", when Marge, Bart and Lisa are at the Fortune Teller's office, you can see the Fortune Teller has three cards in front of her on the table. When Homer arrives, the cards have gone, and later on in the scene they are back on the table again.
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.
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