I think the characters are one level on which Watchmen doesn't work so great as a film. The story is more about ideas than characters, if that makes anysense.
Erik, since you liked the movie so much, I'd highly recommend checking out the graphic novel. I am honestly not a huge comic book guy, haven't really been into them since I was a teenager, but Watchmen is one I find myself coming back to even in adulthood, and I find it enjoyable page after page, no matter how many times I read it. The film followed the comic very closely, but reading it would really add a lot more depth to the film for you.