Crichton says to Rygel, "You, me, and Pilot - we're the only ones who aren't Nebari puppets," to which Rygel replies, "I'm nobody's puppet!" This has a humorous double meaning because the character of Rygel is, of course, played by a puppet.
In the scene where John Crichton tricks Varla into leaving him alone with Chiana, John sings (sort of) "she's gonna get ya get ya get ya get ya...". This is a phrase from the Blondie track "One Way or Another". John previously referred to Varla as Debbie Harry, who is the lead singer of Blondie.