The comic takes a lot of inspiration by part of English folk musician Kate Rusby. Tom is a fan of her.
Sir Eglamore, ("Sir Eglamore") the Annan Waters ("Annan Waters") and Janet Llanwellyn, ("The Maid of Llanwellyn") all take their inspiration from several of her songs.
Lindsey & Bud's names, and the fact that they're engineers in an underwater habitat, to The Abyss.
Tom called Lily "Cookie Monster" when he named her in a tweet. She also shares his color scheme and seemingly has toned-down mannerisms and speech patters of Cookie Monster. She might be also a reference to another Perky GothGenki Girl with much the same colour scheme, perpetual crazy smile and lack of inhibitions in the L.A.W.L.S. comic.
Strip 1013 has Donald (Kat's dad) reading what appears to be The Beano (specifically a Dennisthe Menace UK comic.)
Chapter 37, "Divine", has had two so far:
This page might be one to The Lord of the Rings: Sam unhesitatingly grabs Frodo's hand when he's in the "hospital" in front of all their friends (it was kind of a big deal while filming the movie) while Kat hesitates to hold Annie's hand despite (or perhaps because of) the only people around being Robot, Shadow 2, and Reynardine.