I read this book in a matter of days, because of its page-turning nature. Overall, the story wasn't quite as compelling as the story of the first book. I am still fascinated by the book's heroine, though, as everyone else seems to be.
Without giving too much away, let me say that the mystery in the second book is less complex and layered than the first story. It's a fun ride, of course, with lots of nasty people threatening our hero and heroine, but I didn't think it was nearly as interesting.
Lisbeth Salander's story is fleshed out a bit more in the second novel of the series, and makes her a less mysterious heroine, but no less interesting.
I thought that the end of the first book was slightly abrupt, but in a brave kind of way. The second book, however, ended so sharply that it was obvious that another book was intended to follow. I found that to be a bit irritating, almost as though the author took for granted that we'd be interested enough to read a third book. (I am going to read the third, of course, but I disliked the assumption.)