] Is Denmark the unweeded garden, or is it "this world" in general? We already know that more people than Hamlet think that "something is rotten in the state of Denmark". Is he just re-interating that theme?

I've always taken it as that life has grown into a weeded garden for Hamlet. His beloved father is dead, his mother o'er hastily marries incestuously. Yes, something is rotten in the state of Denmark and the "unweeded garden" could apply to the country, but it seems such a personal pain he's expressing here. He continues on after the "but two months dead..." to eulogize his father and mourn his mother's actions.

I've seen this speech as a set up to the "To be or not to be" soliloquy. Here he is expressing regret that suicide isn't even an option: "Or that the Everlasting had not fix'd His canon 'gainst self-slaughter!" Later he is seriously considering it and has to make a decision - one that could have gone either way.