The title alludes to the controversial 1971 advertising slogan for National Airlines, "I'm Cheryl-Fly Me" which caused outrage with women's rights groups.
While waiting for Banacek to return to his hotel room, Brooke complains to Jay about the scarcity of TV programs available. Brooke mentions a program 'Circus Boy'. Circus Boy was a show that ran from 1955 to 1958. Mickey Dolenz (later one of The Monkees) starred as the lead in the titled role.
The plane Banacek flies in on is a 1963 Fixed wing multi engine Cessna Model 310H, Registration Number N164X.
While talking to the desk clerk Banacek asks about someone named Hester Prynne. The clerk has no idea who he is talking about, not knowing that Prynne was the protagonist of the novel The Scarlett Letter. Banacek says this as a joke, since the owner doesn't allow women in the rooms.