OK, so I'm about halfway through Leviathan Wakes and just about to get to where the show concludes (more or less considering the order of events is different), and while I still am a big fan of the show it's pretty hard to not see where some of the criticisms in this thread are coming from. Since I watched the show first, I can say that I feel the show on its own merits is really good and engaging, but it seems like some of the changes they made were in the interest of making things more dynamic between characters, and while they accomplished that I think they lost some of the wonderful flavor of the book.
More than anything, I have reacted pretty strongly to the differences between book Rocinante and show Rocinante. In the book, Holden is a good leader who has the love and respect of his crew despite still making it up as he goes along. In the show, I don't really see him as much of a leader at all and view the crew more as a group of people that don't quite get along or see eye-to-eye. I mean, Alex is more or less the same, but Holden has a completely different dynamic with Naomi and Amos on the show and while it's certainly more dramatic I guess, I am left liking the book Rocinante crew way better.
Also, something that stood out to me is that the show doesn't seem to be depicting a war between the Belt and Mars at all. Tensions, sure, but no war that I was aware of. In the show, it feels much more like the main characters are trying to avert a war while in the book if feels like they are trying to navigate it and maybe stop it.