That's a really great point about organizing questions. So at what point would unanswered questions get moved to another page? Since for a new blog post, we wanted to have the least friction in getting started answering a question, and if you have to flip to another tab, that might be a barrier.
Your core assumption and basis for Qomments seems to be that the site owner's incentive will always be determined by the number of votes a question has. I don't agree with that, and, prior to being answered, the top-rated questions on AMAs often aren't very interesting. I can only speak for myself, of course; I think people answering would not care about the upvotes, while a company would be more interested in the parameter. The reason being that the number of upvotes are not proportional to how good the question is, but to how many people find it interesting.
In other words, I myself automatically see Qomments in the context of a personal blog, but there are many other purposes for the service.
If Sony were to do a PlayStation-security-breach post-mortem Qomment panel, however, they would be interested in answering the worries that most people share and in putting the FUDs of most people as possible to rest; the voting system has the advantage that it may reveal questions you did not know people had - vital to a company in the eye of a PR tornado. Many commenters (qommenters) also tend to assume that their brilliant questions are unique snowflake, where they usually are not. (Which is why StackExchange uses inline search in the title fields of their question threads. You should probably do the same eventually.)
The latter approach also gives a (better) sense of transparency and user appreciation and participation (think Obama's use of social media in 2008).
Furthermore, compare Qomments to Formspring; when an interesting person has a Formspring account, personally couldn't give a rat's ass what questions have not been asked, so I won't be interested to see those - as a user. On the other hand, the person with the Formspring account would avoid the redundancy of seeing eight million "What is your favourite movie?", but that's only a problem to a person with a large user base. In other words, my personal preference, as good as it is initially, would not scale well; I might as well have people send me e-mails. So I concede to the general wisdom of your default choice - from a general standpoint. My scenario also assumes a very high standard of users, but let's be serious - not gonna happen to most of your clients. Then again, displaying stupid questions/qomments on a site you think highly of might also be a bad idea. The same applies to general comments, of course, but to a lesser extent, I think.
To summarize, there is (1) the approach preferable to a blog article with no visible unanswered questions nor upvotes, and (2) the approach preferable to a corporate of heavily-trafficked site or any site leveraging crowd-sourcing or signalling transparency and user interaction with visible unanswered questions and upvotes.
This means that some might prefer to see - and display - the unanswered questions, while others won't. It probably isn't a matter of what is a good choice and what is a bad one; as long as you include options to toggle either - or provide some nuanced options in between - I think you'll be fine. You could also include the aforementioned user scenarios to explain the service and the arguments for customizing it with or without unanswered questions.
I'd love to expound on this, but for now I think I'll just settle on elaborating on one aspect relevant to your service.
PS: What does "Highlights" mean? Are they all the answers or just some of them? Another name would probably be better. A pet peeve of mine is using "Popular", "Hot" etc. when showing some data where the definition of the terms is determined by some behind-the-scenes algorithms that dilute the meaning of the words even more.