It's funny...I could just copy large parts of my review for The Casual Vacancy here. The Cuckoo's Calling has the same strengths when it comes to character-building. Even though you only see them through the eyes of Strike or Robin the characters really come alive. Many authors have the tendency to info-dump their characters back-stories but not here. You only get bits here and there and you have to piece them together yourself. Some things are left open completely and we'll never know everything about all the characters.
However the book also has a similar problem I already had with TCV and that's the feeling that it's all simply too much. Strike, the main character, has it really bad: he's a heavily- injured war-veteran, describing his family-background as complicated would be one of the understatements of the year and his ex-girlfriend seems to be somewhat emotionally abusive...there were times when having just one of these things was enough for your average tortured crime-novel hero...
Fortunately Robin manages to balance this out a bit as her life is, while not being perfect, much more peaceful than Strike's. However she is often more in the background and doesn't really seem to be an equal character to strike so there's only so much she can do in that aspect.
The characters involved in the murder-investigation are also all messed up to various degrees...admittedly that was part of the point this book was trying to make about celebrity-culture/our obsession with it but it gets a bit tiring in the long run.
The mystery itself was solid, I made some good guesses but did not figure everything out before the end. The novel was also one of the rare cases where I felt equally drawn in by the crime and the characters. Often I end up caring for one thing than the other but not here.