Case Histories, the first Jackson Brodie novel, was Kate Atkinson's first foray out of the world of literary fiction into detective fiction. Unfortunately, it fails very badly as detective fiction.
Some of the flaws stem from the heavy "literary" atmosphere Atkinson is building. This is really a novel of character portraits, to the extent that we're about 2/3 of the novel when Jackson Brodie finally begins to work on all three cases, and the extent of his work is calling around to three witnesses.
But there are also some elements of this novel that are just inexplicable from any sort of perspective. For example, there's a subplot about a threat on Jackson Brodie's life which seems to come from an airport potboiler. It has no bearing on the plot, and enters into the realm of absurdity for a supposedly realistic novel. (Like trying to assassinate a person by dynamiting his house. Seriously. This is the sort of thing you find in a Road-runner cartoon, not a serious novel).
So how is the novel as literary fiction? Well, the above-mentioned stupid subplots have to be glossed over. And you still have to ignore coincidences that would make Dickens blush. And then you're left with a bunch of character sketches that don't really go anywhere, because you've just had to gloss away the little forward motion this novel has.
Maybe I'll try one of her non-detective novels, but I think that I'm done with Jackson Brodie.