I hadn't realized that Moore had written much fiction in the vein of H.P. Lovecraft. Like Campbell or Lumley, Moore has his own voice, but takes much from Lovecraft's themes. There are also constant tiny tributes to Lovecraft's stories, though I don't know how much of that is from the original short story and how much is added in the graphic version.
The Courtyard is set in the nonexistent Red Hook district of New York, and alludes to the Lovecraft story "The Horror at Red Hook" quite prettily, including a conceptually similar protagonist. Instead of a police officer on medical leave, this one is an undercover FBI agent looking into unusual murders. His method of evidence analysis, which he calls "anomaly theory", is pretty straightforward. Look for the weird bits, put them next to each other, and see what stands out. The horrific serial murders he's looking into seem to be committed by various people with nothing in common who don't even know of each other's existence, which seems like as good a place to find weirdness as any.
Our protagonist is also a racist and general bigot. As somebody else's review puts it, it's jarring in several places and the story seems to rub our noses in it rather than just let it be there. While I find his manner inconsistent with the florid nature of some of his narration, this isn't the only dissonant thing in the story, not by a long shot. And knowing Alan Moore, this kind of simple dissonance is thoroughly intentional. It's also possible that some of it is an imperfect adaptation from the short story -- I haven't read it, so I don't know how much is left out by the graphic novel.
I won't spoil the specifics of how Moore adapts Lovecraft's ideas to a modern world. Suffice it to say that they're very intelligent, appropriately ominous, and all-around very Alan Moore. The tie-ins to the real world are done skillfully and with an eye for detail, so it gets more ominous as you know more about what he's alluding to. This is quite simply how a Lovecraft-descended horror story should be told in this day and age.
The constant "quickie" Lovecraft references are maybe a little over-the-top, and the conclusion is done somewhat quickly and abruptly, but those are both errors I'll forgive easily. Both are obviously done for the greater good of atmosphere and pacing, and the Lovecraft references are only likely to come out and slap you in the face if you know his work very well. In fact, many aren't really even to Lovecraft's work, but to other similar works. I hadn't recognized the name Carcosa, for instance, and looked into it only because it was the name of a main character.
Overall, I'm very impressed with the book. I recommend it very highly to Lovecraft fans. I'm not sure how well the premise will work for the uninitiated -- anybody who isn't already a Lovecraft fan want to weigh in?