In general I really like these books, so much so that I actually went out and bought the hardcover of TDE. His world-building (and I mean that in a galactic sense) is fantastic... reminds me a little bit of what's done in the Vor books by LMB but on a grander scale. The history and literature and just the culture that's developed in the background really makes it feel like a lot of time has passed. The stories sometimes get a little too complicated - right now I'm having a hard time keeping all of the names straight - but in general they make for very good mysteries.
The thing that bothers me the most, though, is that the books are so focused on the characters' professional lives. There's really very little focus on their personal lives. For instance, in TDE Chase almost casually mentions that this guy she's been seeing has proposed to her. And when, just recently in the book, Alex gets kidnapped by the cops... well, you know obviously Chase must be upset, but she doesn't say it, or think it, or whatever. Maybe she's just supposed to be this kind of detached personality, but it makes it harder than I would like to get inside her head.
Of course, I'm just a burgeoning Alex/Chase shipper and it would be nice to see her angsting a little bit over his fate.