Peter refers to the baked-goods sex scene in American Pie while speaking to a pie he’s contemplating eating.
Peter starts an organization called the NAAFP "National Association for the Advancement of Fat People", which is a reference to the NAACP; National Association for the Advancement of Colored People. In actuality there is an actual NAAFA; National Association to Advance Fat Acceptance.
A cutaway scene shows the invention of music by cavemen. There was a similar scene in the Mel Brooks film History of the World, Part I. In this episode, the cavemen invent music through grunting, while in the movie one of them invents it by dropping stones on the feet of his fellow cavemen.
Stewie’s “French fried potaters” comment is a reference to the film Sling Blade, in which a murderer who is released from a hospital eats french fries, which he calls “French fried potaters.”
During the cut-away scene of that weird commercial that Stewie saw. It was of the Butter commercial were you only see the people's hands with Butter Spread behind them. This is a reference to those Country Crock commercials.