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.
Revealing mistake: After Homer brings Santa's Little Helper home, Homer and Marge hug, and if you look behind them, the background is upside down. There is a picture hanging upside down, and there is a lamp which seems to be hanging from the ceiling. Then in the next shot, the background is normal.
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.
Audio problem: When Lisa rides past on her Pony, Ralph is sitting on the fence with another boy who says, 'She really tamed that horse', Ralph says, 'Yes but who can tame her?'. However he speaks with a deeper voice as opposed to his higher squeaky voice, and sounds exactly like Nelson Muntz.
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.
Factual error: (Episode 17-1) Alec Baldwin, as an expert on manatees, says that they are also called dugongs. Manatees are found in Atlantic coastal waters and in the Amazon and tributaries. The dugong is a distinct species found in the coastal waters of the Indian and southwest Pacific oceans.