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: 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 the women of the neighbourhood throw Marge a baby shower because she's pregnant with Maggie, Ruth Powers is one of the ladies there. Ruth only met Marge when she moved to Springfield with her daughter in "New Kid on the Block" (Maggie was already born in the episode).