This is quite an accurate adaptation of Tolstoy's 800+ page novel. While there were obviously many changes and omissions, overall, the whole film rang true to the spirit of the book, and I found it very a very satisfying viewing experience.
While most people are aware of the love triangle plotline featuring Anna Karenina herself, the book's main focus is on the life of Konstantin Levin, and what I think this film does so well is to provide more focus on that character and his relationship with Kitty than previous adaptations have done.
In addition, Anna's estranged husband, Alexei Karenin, is usually portrayed as a totally evil villain. His portrayal in this version of the story, though is done perfectly. While we may not appreciate his choices, we are also allowed to see his character in a multidimensional light, which helps make the story more complex and less of a simplistic soap opera.
While the sets and costumes all felt very authentic, I think that what was mostly missing from this were large scale sets to help us see the grand setting of Russia. We needed to see pictures of trains steaming across Russian countryside, we needed to see the inside of an Opera house or two, and we needed to see Levin struggling in the open farming countryside. Instead almost every scene is an interior shot, or a small scale street scene. It is a minor quibble, but without these scenes, I was left feeling that as good as it was, this film adaptation didn't reach perfection liked I hoped it would.