Harry mentions his Trixian saliva mattress, which references the Trixians of the Star Trek universe. Trixian bubble juice was a pink beverage featured on Deep Space Nice. It was Nog's favorite drink (before discovering root beer). His father Rom "borrowed" a case of the pink beverage from the bar owned by his brother, Quark.
When Max says "I saw a movie once, where a person saw an owl, and it meant they were being abducted by aliens" they are referencing the book and film "Communion" written by an abductee Whitley Streiber and starring Christopher Walken. In his description of the owl, it was later to be found out through hypnosis that extraterrestrials usually replace subconscious images of them into an animal which usually is an owl, or deer.
When D'Arcy walks in and sees the alien portal technician, the alien says he shouldn't be seen by humans. Harry tries to cover it up by telling the repair alien that D'Arcy is just in human form and she's really "a slug species from the Arendelle system". Alan Tudyk was in the Frozen movies, which is set in the fictitious Arendelle.