The show is really for people who have read the books. It is accurate to the first novel and even contains a significant amount of dialog from it, but it doesn't frame things as well as George Martin's writing can. I especially noticed this watching the show with my wife (who has not read the books) and having to continually explain things to her that were obviously lacking in the show. Many of the characters actions and some events only seem aligned with the characters if you understand them from the novels.

In short, it lacks the depth that the books provide. This is probably true of most adaptations, but because they appear to be keeping as closely to the book as possible; it is much more noticeable.

As an aside, the Wire is my all time favorite television show.