Though my daughter shun me for blasphemy, I have to say that this was not one of Rowling's best efforts and weak, from a mystery standpoint.
Great characters - if there's one place that Rowling truly shines here, it's in the creation of characters with depth - youthful and bright-eyed Robin, fresh from Yorkshire, battered and grizzled Strike, who though slapped countless times by the hand of fate, proves determined to unravel the mystery of Lula's death and see justice served. If there's anything that propels the reader through The Cuckoo's Calling, it's an ever-increasing affinity for these two characters. It's certainly not the mystery.
If anything, Rowling underwhelms us with a story that consists mainly of Strike venturing from person to person to interview each about the events of the day and night of Lula's death. Lots of sitting in cafes and pubs talking about what might have happened and very little action. In fact, it's not until three quarters of the way into the book that the body of a potential witness turns up floating in the Thames, and there's a surprising deficit of interpretable clues until the very end when Strike delivers a Perry Mason-style soliloquy that magically joins the heretofore disjointed facts of the case into a single coherent picture.
Full review here