The writing has improved from the first book, but there's still a few things that prevent me from enjoying them fully. Brennan still does some ridiculous things, and is often standoffish, but really the writing bothers me the most. Practically every section had a foreshadowing hook for the next ( i.e. "That's not how it went," "The next day we found out who blew up the flight."), clearly frequently enough to irritate me. Foreshadowing can be good, but this was overkill.
And it may be just be me, but I think she attempts to vary her sentence structure way too often, and ends up saying things in very round-about ways. And it tends to be the more mundane details. Like, "Boyd [a dog] set to work, removing my makeup." What's wrong with "licking?" It didn't seem like she'd exhausted any of the more familiar dog descriptors, so it felt awkward and obtrusive. It was worse in the first book, but the sentence structures have mostly improved since then.
I'll continue reading them, because they are interesting tales and well-researched. But I've noticed these enough that they're pulling me out of the story.