When Dirk first introduces himself to Todd, Todd asks him if he has ever successfully solved a case. Dirk mentions there was one involving Thor and another involving a sofa. These are references to major plot points in the second and first Dirk Gently books respectively.
The show was shot almost entirely in Vancouver, British Columbia. This is most notable in the early episodes. For instance, Todd's apartment and all the scenes surrounding it were filmed on the corner of Guelph and Broadway in the late summer of 2016.
In the 2007 radio theatre adaptation of the book, Richard, the reluctant assistant of Dirk corresponding to the series' Todd, is voiced by Billy Boyd, famous for playing hobbit Peregrin Took ("Pippin") in the Lord of the Rings movies, where Elijah Wood (Todd) played Frodo Baggins.
Dirk Gently's name - and by extension the title - is a pun. A dirk was a long dagger and in the 19th century "to dirk" meant "to stab". There is no interaction involving a dirk which may be considered gentle.
There are two references to The Hitchhiker's Guide to the Galaxy by Douglas Adams, who also wrote the Dirk Gently books: The Rowdy 3 consists of 4 members, 5 when Amanda joins them. This is reminiscent of when So Long and Thanks for All the Fish was called "the fourth book in the Hitchiker's Trilogy" and the next book, Mostly Harmless was called "the fifth book in the increasingly inaccurately named Hitchhiker's Trilogy." In the second season, the Boretons had a dog named Agrajag. Agrajag was the name of a constantly reincarnating creature who coincidentally gets killed by Arthur Dent every time he comes back in the third book, Life, the Universe, and Everything.
The code names the military uses for the Project Black Wing subjects seem to be quite literal. The Rowdy 3 are energy vampires who are designated Project Incubus. Dirk Gently is Project Icarus, and his special ability seems to be getting in over his head, because he charges into situations completely unprepared.
Much of the show was shot within the 5 blocks of Broadway - between Guelph & Main in Vancouver, BC. This includes Mt. Pleasant Elementary on whose grounds is found Zachariah Webb/Patrick Spring's lab/Infinite Energy Device/Time Machine/Body-Swapping Gizmo.
During the bridge scene, Samuel Barnett dislocated his right shoulder. Because of this, he keeps his right arm very still in certain scenes through episode 1, 2 and 3. He also had to get a stunt double while filming the fight scene between Dirk and Todd at Todd's apartment.