Hardison introduces himself as Alistair Lethbridge-Stewart. This is a reference to Doctor Who (1963) character Brigadier Alistair Gordon Lethbridge-Stewart (aka "The Brigadier"), who appeared in 106 episodes from 1965 to 1989.
Sophie introduces herself as Jo Grant. This is also a Doctor Who (1963) reference. Jo Grant appeared in 77 episodes from 1971 to 1973.
DJ COM4R4T ("Coma Rat") is a reference to noted EDM artist Deadmau5, who also wears a light-up mask.
After Parker pulls the bottom of her shirt down, Hardison refers to "the Picard tug." This is a reference to the way that Captain Jean-Luc Picard, of Star Trek: The Next Generation (1987), would often "tug" the bottom of his uniform shirt down after rising from a seated position; many fans calls this "The Picard Tug" or "The Picard Maneuver."
Parker's reaction to the horse painting is a callback to The Two-Horse Job (2008), where it's revealed she has an irrational fear of horses.