In the pilot, Brenda tells her date she's a Junior at West Beverly, which means they would've graduated at the end of the second season. They didn't graduated at the end of the third season.
Steve has shaving cream on his ears, but when the camera goes to a different angle the shaving cream is gone, and again when it goes back to the other camera angle, the shaving cream appears again.
In the beginning of the series, Andrea was pronounced "An-DREE-uh". Later in the first season, it starts being pronounced "AUN-dree-uh".
In the first season, Donna Martin's mother was named Nancy Martin, and played by Jordana Capra. When she was reintroduced in season 2, she was named Felice Martin, and played by Katherine Cannon.
Throughout out the series, it's clear that the actors/actresses portraying teenagers are actually in their 20s+. This is done as to not interfere with the schooling of real teenagers and to give the general viewing audience who are teenagers themselves, people to look up too.