For those coming in late, the series involves an elite, goth, kickboxing hacker named Lisbeth Salander (Noomi Rapace) who (often indirectly) teams up with ultra-principled super reporter Mikael Blomkvist (Michael Nyqvist) to solve mysteries involving sex crimes against women and high level corruption in both government and business. I have not read the novels - if you wish to insist they're better in the comments I'll take your word for it. The first film, The Girl With the Dragon Tattoo, had the benefit of character development, showing how this mismatched pair ultimately earned the trust of one another, making tentative inroads into friendship (there was also some garbage about Nazism-motivated sex crimes but it was the least interesting aspect of the script).
The sequel jettisons anything involving character and focuses squarely on the plot - with Lisbeth on the run from the police after being accused of three murders. From the offices of his magazine, Mikael attempts to prove Lisbeth's innocence while Lisbeth - ostensibly on the run but mostly just hanging out in her new, incredibly expensive apartment - uses the internet to find out who framed her. The solution to the mystery is ultimately embedded in the title and a convenient flashback during the opening, and the the story makes almost no new revelations about its characters. Looking back, I'm not quite sure how Lisbeth's tormentors knew to set up a critical incriminating element and there's a series of coincidences that make the world of the movie seem incredibly small, populated by too many characters whose paths have crossed for no discernible reason.
The rhythm of the movie is clue, exposition, clue, exposition and it's not hard to starts seeing the simple and repetitive structure of the film early on. The net effect is that viewing it becomes a slog pretty quickly. Worse, within only one movie, the novelty of Lisbeth Salander has worn off as the screenplay simply uses her as a situational tool: a hacking tool, a kickboxing tool, a photographic memory tool, an awkwardly-staged lesbian sex scene tool. She's less a character and more a thing plugged into the plot to make it go, able to expertly navigate the story until the plot requires her to do something stupid during the climax. Mikael fares worse - there seems to be almost no interest in him so he's relegated to a supporting role in her plot.
The most insulting element of the whole thing is the high-minded (and impotent) outrage on display. The script inflicts horrific sexual and physical violence on the female characters at the hands of cartoonish villains who exist in the upper echelons of society. Easy targets, yes, and maybe potentially interesting ones as well, but the movies have nothing to say about the violence save that there are scary men who do bad things and women are either hyper-functional or victims (or both). I can't decide if the climax of the movie (involving farm house and a "final girl" setup from a horror movie) either goes too far or not far enough in its emulation of grindhouse fare like I Spit On Your Grave or Thriller. Like those movies, this one has the pretense of giving a damn about its characters or their dramas but really it's just about the shock and violent rush.
You can read more of Charles's writing at his blog, Monster In Your Veins.