Really bad comments are not the root of the problem. Simply having large number of mediocre comments crowds out and discourages thoughtful discussion from starting at all.
I'd say:
* create some real cost to making comments
* make bad comments disappear/not display at all with time
* make things less democratic -- to encourage good behavior identify users who have this behavior and make this behavior more prominent programmaticly
For example, bloggers who write insightful stuff on a regular basis should get some sort of bonus when content from their domains is upvoted early on. Maybe each upvote would internally count as 1.5 upvotes for the first 100. Similarly, bloggers who have a reputation for writing linkbait should get some sort of penalty.
Right now you can easily spend ten hours writing an amazing blog post and have it not even make the front page. This provides an amazingly strong disincentive for intelligent people to contribute, especially when the front page is dominated by vapid current events gossip. The heart of the problem is that the current system is set up to reward people for submitting garbage from TechCrunch and to punish people who try to make thoughtful contributions of their own.
Similarly, content that takes longer to read should stick around on the new page for longer. Otherwise the front page gets dominated by fluff. Again, there are lots of people who would be willing to spend 10+ hours writing a 3,500 word essay designed to benefit the HN community, but they don't because they know that there is essentially zero chance of it hitting the front page. Right now by the time the first few people finish reading, it's no longer on the new page so any upvotes basically count for nothing. This problem gets vastly worse as the amount of content submitted increases, so if nothing changes then we're probably only a couple more iterations away from having the front page be dominated by pictures of cats.
On the other hand, I've been ridiculously productive the last few months now that HN is basically unreadable, so maybe the decline in quality isn't such a bad thing after all.