The book was originally intended to be another one of Heinlein's "juveniles", and the first part of the book definitely fits in with that quite well. It definitely seemed very Heinlein-esque at the start. The first slightly incongruous element is the protagonist's focus on music. Music has come up in a couple previous Heinlein books (most notably in "Farmer in the Sky", which is fitting since the protagonist of this book is an ex-Ganymedian farmer) but it's never had such a big focus before. But even so at this point the parts that stands out as the most "not Heinlein" are the occasional references to things like Google and the Simpsons.
Pretty soon though we start to see more sex and drugs and philosophy/mysticism. You could argue that the sex part just fits in with the territory Heinlein traversed in his later years, though it obviously didn't feature in his juveniles, but altogether sex and drugs and music and mysticism are definitely mainstays of the other Robinson books i've read, and it made a slightly odd mix. Also there's a couple casual references to LGBT stuff. I admit i've never read most of Heinlein's later works, so i don't know if that's something he's brought up before or not. But in any case that part was handled rather well. I thought the political diatribe in the middle was rather forced and on the nose, even though i agree with the point Robinson was trying to make. Heinlein certainly was never one to restrain himself from political commentary, but it never seemed quite that blatant to me before. On the other hand i was reading most of the books 30-40 years after they were written, so perhaps there were current political events referenced in them just as obviously that i didn't know about and thus didn't pick up on. It seems a little doubtful though.
But in any case, there were definitely plenty of references to other Heinlein works. Personally i noticed allusions, both blatant and subtle, to the aforementioned "Farmer in the Sky", "Citizen of the Galaxy", "Revolt in 2100", "Between Planets", "Red Planet" and "Stranger in a Strange Land", "The Rolling Stones", "Time for the Stars", and "The Door Into Summer."
About two thirds of the way through the book however it suddenly takes a sharp swerve that proves it's not following Heinlein's "Future Histories" any more and seems much more typical of a modern SF book.
I think i would have been happier if Robinson had stuck to something a little more traditional, but since Heinlein never got the chance to finish it himself who can say where he would have gone with it? Robinson did make a good case in the afterward that it did fit in with some viewpoints Heinlein expressed himself on more than one occasion.
So again, overall i'm happy to have read it, but it's certainly possible the book may give you mood/thematic whiplash. And i'm not sure what to think about the rumor that Robinson may be doing sequels to the book.