If someone is being critical in an unproductive way, then show them the productive way to be critical, and if they fail to shape up, then remove them from the community, through a ban or deletion/hiding of comments.

How specifically? I imagine it would be good to tell certain people: "you have already written twenty comments with almost the same content, so either write a full article about it, or shut up".

The idea is that writing an article requires more work, better thinking, and now you are a person who must defend an idea instead of just attacking people who have different ideas. Also an article focuses the discussion of one topic on one place.

Even if someone e.g. thinks that the whole LessWrong community is Eliezer's suicidal cult, I would prefer if the person collected all their best evidence at one place, so people can focus on one topic and discuss it thoroughly, instead of posting dozens of sarcastic remarks in various, often unrelated places.