Waiting to go public will only cause harm to the site. We have everything we need to be successful: a core group of dedicated community members, a great collection of high-quality questions and answers, and several ground rules regarding sources, acceptable questions, and other topics. What we need now is to start getting more activity, and the only way we can begin to do this is if we go public.
It's true that we still have to work out some issues with our scope, but I don't think those issues can be resolved in private beta: we need a bigger base of content in order to determine what makes a bad question, and we will only get that if we go public.
It's also true that only 85% of our questions currently have answers, but I think that's a good thing. Answers on this site are high-quality and well-sourced. Writing a good answer takes time, especially when the question requires specialised knowledge (which is the case for most questions on this site). The questions that remain unanswered aren't unanswered because they are bad, but are unanswered because we just haven't gotten to them yet.