Continuity mistake: This is a mistake for the introduction for the later episodes. 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.
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.
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. You can see that it says 'Also: The Bee Sharps', only they don't name themselves that until later on in that episode.
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.
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.
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 didn't put it back on, he let it fall to the ground when Bart pulled it off.
Continuity mistake: Marge drops Lisa off at school for band practice, and 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.