On re-reading this classic recently, I was very struck by the clever use of language.
“The Moon is a Harsh Mistress” was first published in 1966, the setting is 2075-6. Heinlein gives his viewpoint character a plausible future Moon dialect of English; a number of Russian words and even some Australian ones such as “cobber”. The character’s speech often lacks the article “the”. I think that is a common characteristic of Russian native speakers because their language is heavily inflected and therefore does not require the constant use of the definite article. So the dialect is plausible in a small future Moon population composed of descendants from many different countries.
The novel launches straight in to a dialogue between this character and a self-aware computer. This beginning was challenging but I found it intriguing. Typically for Heinlein, there is little explanation or description; we learn about the character’s world through watching him living in it.
It is often said that Heinlein’s writing style is so invisible as to be a non-style; I would rather say that the characteristics of Heinlein’s writing are sufficiently distinctive as to constitute a “style”. This kind of discussion often becomes an argument about definitions, but I would say that style is what makes a writer unique, rather than just a competent craftsperson. Did anyone else write like Heinlein? No. You can tell it’s him immediately.
Look at http://templetongate.net/rahstyle.htm for further discussion on this point. Among other things, I agree with the comparison with another genre master, Dashiell Hammett.
S.C. Flynn 
Same here, I was reading and it was hard to follow the sentence structure.
Luckily, I am a native Russian speaker and I caught on what was going on.
The vocab, such as “Ya”, “Da”, “Gospozha”, etc is Russian.
In addition, the feature of Russian language is the free form of sentence construction. You can say “I went to the store to get bread” or you can say “Bread, at the store got”. Anything goes.
Impressive that Heinlein was able to sneak that in.
One negative side effect is the loss in the Russian translations of the book, which I may have read when I was a teen in Russia. (Oh, and we love run on sentences!)