Quagmire’s license plate reading “Bushman” is a reference to the Seinfeld episode where Kramer gets a license plate that reads, “Assman”.
When Peter suggests the world may have been created just for him, a cutaway shows Christof, who controlled the artificial world of the 1998 film The Truman Show parodying the plot of the film.
Peter mentions Scott Baio "plowing a woman he doesn’t love.” This is a reference to the Happy Days actor’s multiple, short-term relationships.
When Peter prompts Joe to be Chris’s father and then Cleveland, a deer walks in to offer fatherhood. This is a reference to the film Bambi.
Peter tries to teach Chris how to eat an Oreo, a reference to commercials of the cookie brand.
When Peter says “Freeze Frame,” and he breaks the Fourth wall, it is a reference to Saved by the Bell. The main character, Zack Morris, had the same ability. At the end of the aside, he urges the viewer to leave, as he is going to “do stuff” to Lois while she is frozen.
Peter asks Cleveland Jr. to call him Mr. Drummond, a character from the 1980s sitcom Diff'rent Strokes, who adopted two African-American children. He later asks Jr. to call him Mr. Papadopoulos, the adopted white father of an African-American child on another 1980s show, Webster.
Paddy has a secret tunnel “like on Hogan's Heroes,” referring to the secret escape hatch of the characters on the 1960s POW camp sitcom.
The beach scene featuring Chris and Quagmire parodies the clothing, music and nonsensical catch phrases of 1960s Beach Party films aimed at teenagers.
Quagmire asks, “Are we in Tian'anmen? Because I see a square!” This puns on the Tian'anmen Square, the Beijing plaza that was the site of a 1989 crackdown on political dissent, and the use of the term square for an uncool person.