In all of the synopses of "The Wrong Case" I've come across, the prevailing attitude seems to be that the story's protagonist, private detective Milton "Milo" Chester Milodragovitch, is unusually flawed and human -- a drunk, a deadbeat, and operating on the notion that he possesses none of the superhuman cunning / guile and perceptiveness of a Sherlock Holmes or even Raymond Chandler's archetypal private detective, Marlowe. I suppose I'd have an easier time believing that if I didn't think it was all a rouse, a suggestion by the character who believes it in part, believes his own misdirection -- that he is not to the caliber of the best detectives. Which brings us to the most effective motif of the novel -- illusion-crafting, myth-making. The characters all seem bound by their desire for the world to be either not what it is, or as I think is true of Milo, they're deluding themselves into believing something false about themselves, something that makes their own failures easier to cope with. The sort of "life mulligan" everyone who thought at one time they might be better than their circumstances tries to claim, mostly with affected indifference or affected-turned-to-actualized-by-rote-effort indifference.
But Milo is nobody's fool. He's depressed and he's an alcoholic. He wants somebody to give a damn about, which makes him interesting in the rough-around-the-ages way typical to antiheroes. As a character study, he's especially fun. Because of his insecurities, which are present from the very first, he never feels like a character you can pin down entirely. Will he choose cowardice? Perhaps, but for the most part he always confronts his attackers, detractors, interrogators, et al, head on -- the only one of these he seems to avoid more often than not is the even more unflappable police lieutenant, Jamison, who's also married to Milo's ex-wife and stepfather to his natural son (Milo has, what's more, an adopted son, a biracial ex-junky who goes by the handle, "Muffin"). Milo's a friend to the dregs (bums and winos, usually they are one and the same) of Meriwether, a fictional town located in the Pacific Northwest and in and around which all the action of the novel takes place.
Some mild spoilers forthcoming:
The impetus of the plot belongs to the entrance of Helen Duffy, a young woman whose looks and charms are enough to insure, in spite of himself, that Milo will assist her in finding her missing brother, not by direct relation but adopted, named Raymond. (The inanity of this exceedingly common mystery trope is undone somewhat humorously with a frazzled Duffy tripping out the door of Milo's office at the end of their initial meeting.) Raymond does turn up later, but dead of an overdose, which Helen refuses to accept was anything but the result of a purposeful murder and continues to use Milo's services to find the culprit. Milo is aided by one of the town's preeminent and most senior drunken bums, Simon, a friend of Milo's deceased father who in certain respects is a surrogate in that way to Milo, although because he shows such a tendency for haplessness in his own right it is more often Milo's responsibility to take care of Simon than receive any useful tutelage from him. Still, their bond is evident right away, and becomes a big part of the pathos that contributes greatly to Milo's character.
That's all I'll say for the essential plot elements, any more would give away too much, I think. And giving away too much is probably the worst thing you can do when describing a mystery novel. Besides, as mentioned already, I'm more concerned with the philosophical elements of the plot -- of what Raymond was vs. what Helen wanted to believe about him, of what Milo wanted to believe about Helen and himself, and so forth. The one thought you are struck by, throughout reading this story, is that there is no way this can end in a conventionally happy way, which that may very well be the case, although I'm not telling.