The story involves the search for what happened to Harriet Vanger, the niece of Henrik Vanger, Swedish industrialist tycoon. Disgraced journalist Michael Blomqvist is hired by Vanger to research her disappearance and presumed death 40 years earlier after so many others have failed. Blomqvist requests an assistant with computer/internet skills (read hacker) and Lisbeth Salander is hired. Both are intense, intelligent, independent individuals who are quick to intuit and inevitably become involved.
Niels Arden Oplev's direction of the original movie, 152 minutes long, was very faithful to the book. Its depictions of violence, sex and sexual violence leave nothing to one's imagination: it is very graphic and detailed indeed. Fincher's version, six minutes longer at 158 minutes, while remaining true to the spirit of the novel and telling of the story, shows the sex, violence and sexual violence but assumes the American audience can neither tolerate it as much nor as long nor in quite so graphic detail. The screenplay takes a few shortcuts that don't affect outcome of the story or the setup of the remainder of the series.
Trent Reznor (of Nine Inch Nails fame) and Atticus Ross were responsible for the original music. They have worked with Fincher before, most recently on The Social Network.
Positives: Daniel Craig does a nice job. Not a fantastic, Oscar worthy job, but he gets out of his clothes often enough to keep me interested. Not sure if that does much for any of you folks, but it made me happy. Rooney Mara was effective, her performance was more emotional than Rapace's, if it can be called that, as a character such as Lisbeth Salander is not one to show emotion. Always nice to see Robin Wright, here as business partner to Daniel Craig's character. Other actors were all good.
Overall, I give the movie a B+. If I had to pick one movie, I would recommend the Swedish version. But if you are a true fan of the novels, see both.