You have to view an individual comment to get the flag option. I'm not sure what the down votes are for. "This comment does not belong on HN", maybe.
I have no idea what the flag is for. "This content is so bad it needs to be removed, not just hidden", perhaps.
I agree with your post though! I'd be wary about having too many options for marking posts.
My observation is that downvotes also signify comments that have one of more errors of fact. Of course "fact" is also open to interpretation and not absolute.
You could say "you can only be President for two terms of 4 years each" but someone could dispute that because Roosevelt was President for longer or because in their country that is not the case. Etc.
A downvote because of inaccuracy without a comment isn't very helpful of course.
I do most of my reading on Reddit (front page reddits are just cotton candy, but there are good ones to be found). I only started reading HackerNews about a year ago, and mostly just for the articles from lesser known blogs that don't get posted on Reddit. Being something of a HackerNews newbie I haven't been around long enough to notice a change, but I hope it doesn't go the way of Slashdot.
I know that the worst offenders won't read the guidelines, but a little faith in the rest of them would go a long way improving the quality of content on this site.
There is not going to be a "one-size-fits-all" solution to this problem. A multi-faceted solution including both technical and non-technical elements would likely work best.
The easiest part of the solution to implement would of course be the text in the vicinity of the comment box. This text would establish certain core tenets that we can all vote on with Paul.
The technical aspect of the solution could monitor how often certain users are being down voted. The down-vote history of an account could then be used to "weigh it down" somewhat, so that it takes more up-votes in the future to bring their comment to a higher position on the page.
So long as it is a group norm to do adhere to the guidelines those who don't will be downvoted and their conduct will have little influence on the community.