Video Continuity mistake: This is a mistake for the introduction from seasons 2-20 (1991-2009). When Homer screams, he turns round. You see this in a wide shot. There are no boxes to the right of the door in the garage. However, two just appear out of thin air when he runs through the garage. (00:01:50)
Continuity mistake: When Homer's Vegas wife shows him the video in front of Marge, it shows Homer kissing Ned. This didn't happen when she showed it in the Vegas episode.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: Lewis changes from black to yellow when Milhouse dares Bart to pull Santa's beard off. (00:14:10)
Homer's Barbershop Quartet - S5-E1
Continuity mistake: When you see a shot of the church from outside in the scene where the bee sharps sing there, look closely at the sign. It says 'Also: The Bee Sharps', only they don't name themselves that until later on in that episode.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: While having breakfast, all of the Simpsons' glasses of orange juice keep disappearing and reappearing throughout the scene. (00:05:35)
Hamster
Video Continuity mistake: When Bart leaves the school, you can see that his skateboard is green and perfectly flat. But when he is skating through the crowd and past the people at the bus stop, the skateboard has an orange stripe down the middle and is raised at the rear.
The Girl Who Slept Too Little - S17-E2
Continuity mistake: At the end of the episode where Homer is on the field talking to Buck the baseball player, the stadium is crowded. When Homer and Marge are leaving in their baseball golf car one second later, the stadium is empty. (00:20:40)
Andreas WinnbergThe Bonfire Of The Manatees - S17-E1
Continuity mistake: When Marge is in the car upset at Homer, the door to their house changes from open to closed then open again between shots.
Video Continuity mistake: When Maggie goes through the checkout at the beginning, Marge's trolley is grey and has a red handle. But in the next shot, when Maggie pops out of the bag, the trolley handle is turquoise. (00:00:30)
Hamster 
Video Continuity mistake: In the introduction, initially Maggie's seat is light purple. However, in the wider shot of her and Marge, the seat changes to a burgundy colour. (00:00:50)
Continuity mistake: In the bit where they sit on the sofa at the start of each episode, there is one rather long one where it starts off with the Simpsons dancing in a line, then gradually evolves into a circus with elephants and men dancing around fire. Look closely in between Homer's right leg and the dancing woman on his right. There is a pile of books on the little shelf underneath the lamp and telephone, and just as the camera starts zooming out from the line of dancing, the orange book on the left noticeably changes to purple. (00:01:20)
Continuity mistake: The notepad Homer draws the blueprint on changes from having content on it to being blank so he can draw on it.
The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: When Homer walks out Circus of Values with his purchases, he bumps into Flanders, and all the presents scatter everywhere. Watch out for a red present with a green bow that goes flying near the left hand side of the screen. As soon as it hits the ground it turns into a pink box with a white bow wrapped around it, with no shot changes. (00:10:15)
Hamster The Simpsons Christmas Special: Simpsons Roasting on an Open Fire - S1-E1
Continuity mistake: Bart yanks Homer's beard off in the mall, Homer then takes Bart into Santa's workshop. When they are inside Santa's workshop, Homer's beard is back on, despite the fact that he let it fall to the ground when Bart pulled it off.
Moaning Lisa - S1-E6
Continuity mistake: Marge drops Lisa off at school for band practice. She walks up to the entrance steps, and then converses with two boys. Then her teacher comes up, and Marge gets annoyed. When she comes to grab Lisa back into the car, Lisa is right by the roadside, along with the two boys and the music teacher.
Treehouse of Horror XVIII - S19-E5
Continuity mistake: When Marge puts the logo Hugh Laurie in the microwave, he splatters in the corner. Next shot the splatter is in the middle of the microwave. (00:01:00)
Ssiscool 
Video Continuity mistake: In the old main title sequence, when Homer gets out of his car, the door inside the garage is red, but when he is screaming and running towards it, it's now brown. (00:01:40)
JonTheRandomPlease Homer, Don't Hammer 'Em - S18-E3
Continuity mistake: It is revealed that Bart is very allergic to shrimp. However, in "The Frying Game" (where Marge and Homer get "framed" for a murder and end up on "Frame Up"), Bart says he was in the green room and that he "ate so much shrimp."
Continuity mistake: On various occasions The Front door, viewed from the inside of the house, has hinges - and therefore opens - on the wrong side, if you compare it to the shots of it from the outside.
He's My BrotherThe 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.
OL1V3R666
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.