As murder mysteries go, The Coroner is better than most. Sure, the plot is necessarily formulaic, but the characters are believable and interesting. The over-arching storyline was compelling enough to make me look forward to reading the next in the series.
I can't point out weaknesses in the plot without spoilers, so I'll nitpick the editing instead.
1. The book starts strong with medical descriptions that seem to be pulled straight from one of the better forensic/medical TV dramas. Technical enough to be interesting and make you feel smart, but not so technical to lose the lay-reader. The end of the book, however, goes the opposite way. There are clear medical crises going on, but we only get vague descriptions of their effects...which are substantial.
There is a line between being severely injured and being dead. I can't tell you where the line is, but a fictional character who performs both life-saving surgeries and autopsies should be able to. What happened to her medical expertise? Why can the narrator at the end of the book no longer explain what's going on? I'm guessing it was a deadline issue?
2. I am incredulous that the editor did not catch at least two misuses of incredulous. When the main character receives a text with unexpected information, the narrator tells us that "this was incredulous." Simple mistake. No big deal. But a few chapters later, it gets repeated when the narrator tells us, "It was incredulous to think that..."
I know this usage may be creeping toward respectability, but my Dictionary of Modern American Usage (admittedly from the previous century) tells me that amazing facts are incredible; people who are amazed to the point of being skeptical of those facts are incredulous.