This review will contain spoilers!
In many sentences:
I enjoyed this book a lot, much more so than Stranger in a Strange Land, which is the only other book by Heinlein that I've read. First of all, the story itself is really interesting, and really well-paced. From the introduction of the sentient computer and its strange sense of humor, to the way all the political decisions, subterfuge, and war are reasoned out in a logical and thoughtful manner, there's really nothing to complain about in regards to the plot.
I also really liked the way Mannie came through as a character from the very beginning through the sentence structure. Quite often a single word would be missing from the narration, allowing the Russian influence of Mannie's dialogue to become present. It was a really nice touch and something that didn't get old, even at the very end of the book. It also felt consistent, which must have been tough to carry off throughout the entire book.
Heinlein's ability to consider so many qualities of life on the moon was also really impressive. Everything from marriage systems when men far outnumber women, to shipping grain to Earth by using Earth's large gravity well, and the idea that even ex-cons on would become friendly if living on the moon because if you aren't, it's a simple matter to eliminate you by tossing you out an air-lock. There are so many little things in this vein that I can't list them all, but it really brought the world of Luna to life in a very enjoyable way.
My only real complaint is so minor that it's not really worth mentioning, but some of the Loonie phrases struck me as juvenile and annoying (the most egregious being "talk-talk").
One other thing I wanted to mention - I often think in book's like this with a lot of logical back and forth over determining the likely outcome of a very complicated scenario that, while what I'm reading seems reasonable, in reality there are so many other possibilities that if I stopped to really think about what they are proposing, it would be very easy to argue against it. At the same time, I don't really care if this is the case because what I am reading is reasonable and entertaining, so who cares? Orson Scott Card's books make me think of this every time as well.
I think any fan of science fiction would enjoy this book even if, like me, they disliked Stranger in a Strange Land.