Genius Bonus: If you have a solid knowledge of history, literature, music, hypothetical physics, and computer programming then you're in for a treat.
Dirk's ramble about St Cedd "one of the duller Northumbrian saints. His brother Chad was even duller. Has a cathedral in Birmingham, if that gives you any idea." St Cedd's College is fictional, but its namesake was real, and was indeed the brother of Chad of Mercia, whom St Chad's Cathedral is named after.
Recycled Script: Douglas Adams, who liked to recycle plot elements, based the first Dirk Gently book on two of his Doctor Who scripts: "Shada" and "City of Death". Knowing this helps explain one of the stranger assumptions in the first book: just why Professor Chronotis happens to be a centuries-old man who lives in a time machine. (It's because he's a retired Time Lord.)
What Could Have Been: The Salmon of Doubt anthology features the beginning of a third book that was never written. And its style is so instantly familiar that it feels just like the other books. Then it stops. Just after Dirk has flown to America and encountered a truck carrying a rhinoceros to an unknown destination.
The TV series
Affectionate Parody: Of Sherlock, at times, such as Dirk describing a case as "boring" only for it to turn out to be relevant to the conclusion of the case he's working on.
The visual style of the first episode feels like a piss-take on Sherlock, with its zooms and close-ups on specific words/clues. Also, Dirk possesses knowledge about all of the intricate details of a case (as does Sherlock), but is often wrong about them until the very end.