Continuity mistake: When George and Homer burst out of the manhole, there is a shot of the Simpsons' house covered in mud, then a quick one of it totally clean, then another when it's muddy again.
Raging Abe Simpson and His Grumbling Grandson in 'The Curse of the Flying Hellfish' - S7-E22
Continuity mistake: Grampa loses his red slipper as he is pulled by Mr. Burns' boat. Later it is back on his foot.
Much Apu About Nothing - S7-E23
Continuity mistake: When Barney is tranquilised, he falls with his mouth closed. In the following shots, it's open, closed, then open again.
Tree House of Horror VI - S7-E6
Factual error: In "Nightmare On Evergreen Terrace", Martin has a dream, in which he speaks Latin. At one point, he says a verb that doesn't exist: "morire". The words is "mori" (to die), "moritur" (noun dies) or "moreris" (you die). The "moirie" is also on the blackboard behind Martin. (00:08:20)
Much Apu About Nothing - S7-E23
Continuity mistake: When Homer swings on the electric cable when attempting to get to his car, the cable has just appeared from nowhere because, the previous 'birds eye view' shot showed no cable.
Much Apu About Nothing - S7-E23
Continuity mistake: When Ned is struggling to get in the house at the beginning the door knob is light brown, then dark brown in another shot.
Continuity mistake: When Lisa first discovers Jebadiah's confession, she is holding the fyffe and wearing his racoon hat, the screen fades to black (I'm guessing for the ad break) but when it comes back Lisa is standing in exactly the same position, still reading the confession, still holding the fyffe, but no longer wearing the hat.
Continuity mistake: When Lisa knocks the lamb chop out of Bart's mouth to Homer's it changes colour during the journey.
Much Apu About Nothing - S7-E23
Continuity mistake: When Apu introduces Professor Frink there are people either side of him but no Apu. In the very next shot Apu has appeared from no-where and is standing beside the Professor.
Much Apu About Nothing - S7-E23
Continuity mistake: When the mob come back to Quimby to complain about the 'Bear Tax' he opens the left door inwards.In a following shot both doors open outwards.
Tree House of Horror VI - S7-E6
Factual error: During the "Attack of the 50 ft. Eye Sores" segment, the family steps into the footprint of the giant donut guy to look at the label. The label should appear to be spelled backwards, but it was not.
Continuity mistake: In the Meat video Jimmy's steak is first seen to be a little thin. In the closeup it's very thick, then thin again in the next shot.
Continuity mistake: When Maggie's dummy is spinning after the goat has taken her, the ground is clear. In the next close up shot there are tufts of grass and clumps of dirt there.
Audio problem: Just after Homer has been knocked down by the cannon with the "No Litter" message on his stomach, you hear cheering but the crowd don't do anything.
Much Apu About Nothing - S7-E23
Continuity mistake: When Apu awakes, he has a closed note pad, and the table looks small. In the next high-angle shot, Apu's book is open and face down, with paper on top of it and a pen beside it. The table is also bigger, with Bart sitting there with his breakfast things too.
Continuity mistake: When Homer and Lisa are trying to convince The Town board to dig up Jebediah, members of the board keep disappearing.
Continuity mistake: When Lisa starts to drive away with Homer's pig, Marge is screaming 'No.' On Lisa's close up we can see Marge briefly to the left of the screen and her mouth isn't shouting.
Factual error: If Homer's stomach was really caught on the towel rail the way they show it to be, he wouldn't be able to see the scales at all without having to look round it.
Much Apu About Nothing - S7-E23
Continuity mistake: When Nelson pulls back Uta, he drops a book. In the next shot, the book has gone.
Much Apu About Nothing - S7-E23
Continuity mistake: When Apu and Lisa go to the 'Immigration Centre', they pass Dr Hibbert on the right, and he has yellow skin. In the next shot, his skin returns to its proper brown colour.
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