Factual error: After Bart's prank call with Moe, you can see Bart and Lisa laughing. However the telephone's wire does not connect to the receiver. (00:09:40)
The Last Temptation of Homer - S5-E9
Continuity mistake: Mr Smithers throws a notepad at the person saying that a real emergency exit is required, but when we see it on the floor it is now a book with a green cover.
Continuity mistake: Near the start, when Homer is going through the medicine cabinet and we see various items. He takes out various hair growth products, and then when we see what's left, the floss has vanished. (00:01:10 - 00:02:20)
Tree House of Horror XII - S13-E1
Audio problem: In 'Wiz Kids,' when Edna asks Harry Potter if he is chewing gum, he replies "No ma'am, it's brimstone," however it's clear that a different line was originally intended. (00:15:25)
The City of New York vs. Homer Simpson - S9-E1
Continuity mistake: Just before Homer tries biting off the boot, he is wearing a watch. But from then on it disappears off his arm until he is trying to figure out how many hours it is from 9-5.
Homer's Barbershop Quartet - S5-E1
Continuity mistake: In the flashback where Marge is making a model of Homer, the models head falls off and Santa's Little Helper picks it up, but the Simpsons did not own the dog back then.
Plot hole: It is shown that Marge first met Luann van Houton when she was ten. But in "Homer Defined", Marge said that she first met Luann in an emergency room when Bart and Milhouse drank paint.
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?
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