While we already have plenty of people interested in the topic and good at doing research (overflow from other SE sites), it seems like this site won't succeed without "real" experts: professors, theologians, seminary students, and pastors. What can we do to spread the word in those circles?
This is a problem with all Stack Exchange sites. The answer is that we need to "market" the site (for lack of a better term)
Generally this is accomplished by posting links to the site or to specific questions on social networking sites. For example, if you know a place where biblical experts hang out, post a link to a question asking for answers or opinions. It will draw the experts to this site.
Another way to draw people (in general) is by using this site to answer questions they may have. For example, if you have a friend who is struggling with the concept of fear, forward them the link to the question about fear: How can we understand “fear”?
Also, we can email experts directly, asking for their opinion on a certain topic. So, if you see a question pop up and you know an expert that could answer it well, send them the link to the question.
Finally, ask good questions. When experts use Google to search for a given topic, what are they searching for? If you can ask questions that experts would ask (in the manner that experts would ask), then they will find this site through Google. (In fact, Stack Exchange truly desires 90% of all site traffic to come from Google or other search engines.)
Essentially, we need to get out there and "spread the good news to all the nations". Err... well, you get the idea. Just "market" the site, the questions, and the answers and we will draw the experts.
Also, ask excellent questions and post excellent answers and they will come (slowly but surely).
One encouraging thing I've noticed about this site that is that we have a relatively high unanswered question rate. Yes, I think that is a good thing. The reason they are unanswered is important here. If they were ignored because they were low quality we would have a problem, but if they are good questions that are just waiting for the right experts to come along, I think that is a good thing. This will do much to attract good experts.
Sure, those question need answers eventually. But this suggests two things we can do.
Find good questions that don't have good answers yet and ask ourselves "Who can best answer this question?", then take it to them and ask them to contribute an answer.
Don't encourage half-baked answers. Lets not be about blurting out best-guess answers just to get the question out of the way.
In the hope of getting more help on Jewish sources, I've taken the liberty of posting a question on the Judaism meta asking for help. Has someone done the same thing on the Christianity StackExchange? Are there other sites we can draw from?
Back when it was still a proposal, I forwarded it to our senior pastor and a few others from the church that I thought might be interested. (Our pastor is at a conference this week; he committed to the beta but obviously probably hasn't even seen the invitation yet.)
Once the site is public, you can do the same with people you know.