The title refers to the "Peters Principle" which states that, in business, people are promoted past their level of competence. Not unlike how Peter Griffin keeps getting jobs he is in no way qualified for, like that of school principal.
The Phil Collins song Joe refers to is 'In the Air Tonight.' The story he tells about the origins of the song is a popular urban myth.
Peter walking around with a baseball bat is a reference to real-life principal Joe Louis Clark, who inspired the film 'Lean On Me.'
From this episode onwards, Donna Tubbs took Jillian's place in the title sequence. This makes perfect sense since she's married to Cleveland, due to the supporting cast being parallel to their significant other (i.e Joe Swanson and Bonnie Swanson).
The Principal's secretary is played by Wendy Schaal, who voices Francine on 'American Dad,' another animated sitcom created by Seth MacFarlane.