Let me respond to each of your points seperately.
The quality of questions seems to be very low[.]
I agree. We definitely need to raise question quality. A good question should be detailed and well-researched, just like a good answer should be. I try to set an example of that with my questions, and we should encourage more users to ask questions like those, as opposed to "What does Hinduism say about X?" type questions. This point has been brought up before, in this Meta question for instance.
[S]everal posters seem to either be playing the fool or are non-Hindus trying to poke holes in our doctrine and popularise these misconceptions.
First of all I think Hindus make up the vast majority of our user base, but in any case we welcome the participation of non-Hindus. While this is a site about Hinduism, this is not a Hindu website. This is a site where people can ask and answer questions about Hinduism, even if they don't believe in it. Now spreading misconceptions is obviously not a good thing, but if you see an answer with wrong information, then suggest an edit, downvote it, comment on it, or post an answer of your own. The best way to fight falsehoods is with truth.
Sadly, noone on this forum is an authority on the scriptures who can provide "dharma sandeha nivrutti".
Well, whether we have "authorities" or not, we do have some users who are relatively knowledgeable about Hindu scriptures, although of course we should try to get more.
I recommend that for the time being, we limit the topics on which to ask questions. For e.g., they have to be limited to the scope of the purANAs. If we leave the scope so broad as to include veda, shat sastra, upanishad, janAchAra , dEsAchAra, superstition etc., we are doing a great disservice to this topic and our religion.
I don't think that we should limit questions just to one scripture or category of scriptures. But what I do think is that users should try to ask questions that are grounded in scripture. For instance, questions that ask about a particular quote from the Vedas, Puranas, Ramayana, Mahabharata, etc. That should help raise question quality.
It may not be a bad idea to recruit established panDitas to spend some time each week to provide authentic and authoritative answers.
Yes, I agree. It would be nice if we could make fliers to post in temples and other places, to encourage more experts to sign up.
Lastly, we need better moderation please. Current set of moderators, while well-meaning, are clearly out of their depth.
Well, I've never been a moderator before, so it's certainly possible that I'm out of my depth. But I think the moderation team as a whole is doing a great job. But you can help the moderators do a better job; if you see an issue that could use the assistance of a moderator, just click flag button on the relevant post(s). Together, we can make this a fantastic place to learn about Hinduism!