The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Mr. Burns comes on the P.A. system Homer started eating a donut, he takes a bite and after that the donut stays the same size even though he takes 2 more bites. (00:06:40)
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: Marge walks through the doorway from a room with a piano, beside a bare wall, and on the piano are two frames and music sheets. But when Marge turns the jar upside down, there is a large picture on the wall beside the piano, and the music sheets and frames have disappeared from the piano. (00:08:00)
Continuity mistake: In the new opening credits (from Feb 09) when the camera is zooming into the bullies cutting the head off the statue Ralph Wiggum is nowhere to be seen, but when the head falls off, it lands on Ralph. (00:00:10)
Continuity mistake: The lettering on Smithers' desk name plate changes between shots. While he is taking the call from Mr Burns' mother you can see his name "W. Smithers" in black letters. The shot after seeing Burns, who keeps falling asleep, the letters are now red.
And Maggie Makes Three - S6-E13
Continuity mistake: When Homer remembers finding out that Marge was pregnant with Bart, he screams, tears out his hair and runs upstairs, past a picture of Lisa in the pink hat she wears to church. This mistake re-occurs seconds later when Homer remembers finding out Marge was pregnant with Lisa. Hard to have photos of Lisa on the wall before Bart and Lisa were even born...
Tree House of Horror VII - S8-E1
Continuity mistake: In 'The Genesis Tub', in between Bart taking the tub and the school science fair, Lisa's slippers disappear from her feet.
Tree House of Horror V - S6-E6
Continuity mistake: In "Time and Punishment", when Homer returns to the basement after his first time travel, there is a scorch mark on the work bench where the toaster was placed when he turned it on. The angle changes to a shot from the stairs, and the scorch mark is gone. Later in the episode, the mark is back on the bench.
Million Dollar Maybe - S21-E11
Continuity mistake: When the bulls are stampeding, people who were at the top of the stadium and safe can be seen running in front of the bulls.
The City of New York vs. Homer Simpson - S9-E1
Factual error: The windows of the World Trade Center couldn't open and the Twin Towers weren't in front of each other as depicted in this episode. They were at an angle.
Grandpa vs. Sexual Inadequacy - S6-E10
Continuity mistake: Homer leaves the Simpson house to go to the farm house in the station wagon, and when he parks in front of the farm house he's driving his pink car.
And Maggie Makes Three - S6-E13
Continuity mistake: Bart comments on Homer's extreme reaction when he realised Marge was pregnant with Maggie. In the next flashbacks, when Homer reacts in the same way to hearing about Bart and Lisa, they are shown in the house at Evergreen Terrace both times. In Series 4, in the episode Lisa's First Word, they show that the Simpsons did not move to Evergreen Terrace until just before Lisa was born. Other episodes have also shown that Homer was with Marge at Doctor Hibbert's when she found out about her other pregnancies.
The Two Mrs. Nahasapeemapetilons - S9-E7
Audio problem: When Homer is running for the food, after racing in the wheelchair with Jasper, he says 'Eat my dust' but his lips don't move for the 'my dust' part.
Continuity mistake: Millhouse is in the classroom at the beginning when Principal Skinner says that superintendent Chalmers is coming for a surprise inspection, but when they show Nelson he is getting crud put down his shirt. How could he be at two places at once?
Audio problem: Just after Mr Smithers says "...so that we have the energy to from your favourite video game to yummy cotton candy machines", all the children start clapping but the sound of clapping starts BEFORE they start clapping. (00:05:05)
Grandpa vs. Sexual Inadequacy - S6-E10
Other mistake: Look closely when the clerk scans the books. Ueberroth is a brown book, and Al Gore's book is green. The book that sends the message to Al Gore is the Ueberroth book.
Continuity mistake: When Millhouse is being chased outside by a sun ray, the ray burns the pavement. It then turns around, and the pavement is now no longer burned. (00:01:40)
Children of a Lesser Clod - S12-E20
Continuity mistake: When Ned Flanders is asking Homer whether or not he is running a daycare centre, there is a radio behind him. The aerial on it changes position in subsequent shots.
Continuity mistake: When the Flanders and Simpsons first meet at the golf course, Flanders is wearing his usual long-sleeved green sweater over his shirt. After Homer says to him, "The fruit of my loins can beat the fruit of your loins any day of the week", the color of Flanders' sleeves is missing, making it look as if he's wearing a sleeveless pullover.
Other mistake: While Homer is in Lisa's bedroom trying to make things right with her, there are three pictures taped to Lisa's mirror. After Homer tells her the music may help, in the next shot Homer walks over to stand behind Lisa. Those pictures taped to Lisa's mirror are weirdly behind Homer's reflection, as if the pictures are taped to the wall behind Homer. Three shots later, when Homer tells Lisa he can fix the dollhouse, his reflection is accurate in relation to those three pictures taped to the mirror. (00:19:20)
Tree House of Horror VII - S8-E1
Continuity mistake: In "The Thing and I": After the kids have found Hugo in the attic, when Marge and Homer return home, both front door knobs (inside and outside) do not have backplates, but once Hugo escapes both door knobs have backplates. The two backplates vanish and reappear repeatedly in following shots. It's funny because when they leave to search for Hugo, Homer shuts the door with no backplates, but then Bart uses a key in the backplate to lock The Front door.
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