I read a lot. When I was a kid, I read a lot of science fiction. In my late teens, I largely switched over to mystery novels. I still love science fiction, but my father reads mystery novels, and his father before him, and presumably his father before him, so I got sort of "non-peer" pressured into them, and I enjoy them. I also enjoy mystery movies and TV shows, especially humorous ones. I'll buy Monk, one of these days.
One of my favorites is Rex Stout, best known for his "Nero Wolfe" novels. Unknown to just about everyone, he also wrote a much smaller number of "Tecumseh Fox" novels.
There are three facets of each mystery story, not counting humor. These facets work together to make a perfect story. Perhaps they could also be expanded to ALL stories, but for mystery novels they are distilled into their purest form.
The three facets are: Characters, an Interesting Situation, and an Involving Hunt.
Some authors excel at one or two of these, but very few get all three. Rex Stout, for example, really sucks at writing involving hunts. His situations are often interesting - one of his Nero Wolfe books is about Wolfe blackmailing tha FBI, another is about cracking a bizarre "reverse copyright" ring. His characters are always good, with Nero Wolfe being the stage onto which all characters are called, and Archie being the spotlight to throw them into relief. But, man, his hunts are never involving, ever.
You see, in order to have an involving hunt, there needs to be something personal at stake for your window character. Mystery novels generally have one window character: unless you're telling a story within the story, it's highly unusual to have more than one point of view. In the Nero Wolfe books, our window character is Archie. Everything we feel, we feel from the point of view of Archie.
Unfortunately, Archie is largely impervious to involvement. His emotions are portrayed somewhat impersonally, even though we stand in his shoes. It is rare that he gets injured or even significantly irritated. Obviously, when the worst a case has to throw at him (and through him, us) is an overnight stand in prison, we don't really feel a lot of involvement in the hunt.
One subgenre of mystery focuses almost entirely on the hunt: Noir. Noir is a genre on its own, and although it doesn't always revolve around a mystery, it usually does. In noir-style film and stories, our window character falls in love, gets beaten up, is totally outmatched, gets betrayed, and perseveres. The window is fully involved, and therefore, so are we.
Unfortunately, most noir films are painfully short on the other two facets, with uninteresting characters that have uninteresting interactions, and plots that come straight out of the weekly police blotter.
But back to Rex Stout. In Nero Wolfe, the shining strength is the way he gives his stories a bedrock. Everything revolves around Nero Wolfe, BUT HE IS NOT THE WINDOW CHARACTER. If you read my post on perfect patterns, Nero Wolfe is a dominant pattern that everything else in the book is related to. This keeps the book focused while also giving us a great way to stir up character interactions and prod a limping plot along. The importance of having this kind of system cannot be overstated: the real weakness of most mystery novels is that they don't have a core.
Noir's core is the involvement in the hunt: it always circles back to revolve around our window character. Thus the endless monologuing. In Nero Wolfe, he seperates the window character from the bedrock, providing a wonderfully unique set of interactions.
It is clear Rex Stout didn't know what he did. He rarely takes real advantage of the situation. His other mystery novels, notably Tecumseh Fox, suffer from having no core. Fox is essentially Archie without Wolfe, and that means Fox is a hunter without a home. Fox wanders from page to page. The hunt is noticeably better in these books, but the character interactions are limp and without any of the glorious fervor we got from Wolfe.
To touch on Monk, and other detectives like him: the weirder and more personally crippled the detective is, the easier it is to discomfit them. That means it's easier to make it an involving hunt. But they HAVE TO BE WINDOW CHARACTERS. Wolfe is easy to discomfit, but we don't care. In fact, we rather enjoy it. Archie is our window character, and Archie is functionally invulnerable.
It's been a disjointed ramble, but now you know more about Rex Stout and the core dynamics of a mystery novel than you ever needed to!