Part of what I DO like about Facebook is the sense of activity. First impression of the main page of the forum is a dead zone. It feels like a sterile directory, with no real direction to go in unless I'm specifically thinking of a topic. In order to encourage people to contribute their knowledge, a recent and trending topic section could help and foster interaction

another helpful feature could be to make the Unread Posts screen sortable by Views, Replies, and Last Post.

"trending" topics is only of use if you're more interested in what other people are interested in, as opposed to what you're interested in. Or if you're interested in moneterising user metrics, or gauging how successful your social engineering/manipulaiton attempts are.

If you're interested in it, you'll find it soon enough.

And it's not a dead zone on the landing page to forum, it just doesn't attempt to try and think for you. You should be doing that. You should certainly have some direction to think in before you even consider a post outside of the "general" section.

Not having something to encourage random people to randomly post isn't a bad thing. It means we'll end up with content people have actually thought about, hopefully. A lot less "me too" posts and more sensible ideas.

On this idea, I find it sort of interesting what the League of Legends boards forums did.
Whenever inside a subforum, you can choose to sort the topics by:
Highest number of votes(could be split in all times, this year, monthly, weekly and "today") Hot(Trending), Recently commented and Most Recent.

With highest number of votes, we have a reason to add an upvote system, we can decide if a "downvote" would indeed be needed(Maybe...), but having people able to provide feedback to one another is indeed useful. With 4 gradations of, people would have a way to know which topics are having the most acceptance by the votes, but it would not be a stale, as even the all-times would move from time to time, as people can still see which received the most votes within a fixed time period.

Trending could also have such a timely system, so we could see which topics have been trending today, this week, month, year or all times, with trending being graded by the comments or by a ratio comment/vote/views, so there are two ways to see how popular a topic really is within different time periods. One possibility is also to add other time periods, such as "1[#] [Week] ago" which would also make it easier to find a topic even if you don't remember its name for the incoming search system.

Recently commented and Most recent are self explanatory, but I think it'd be more interesting if, instead of being two separate options, if they were a single tab with a small section of 5 to 10 topics organized by the most recently commented and under it a second bigger section with the most recently created. And I'd also like to state that I think it more interesting if whenever entering a sub-forum, you were always entering through this tab, so you'd see both the most recent comments and most recent topics at the same time and then you'd choose to organize by trending or votes, which would give a chance for any newer topic to be seen and grow in popularity at all times, giving less chance for good topics to disappear.

If this system is interesting, I do have a complementary suggestion for this, which would be "suggest topic", where a friend or specific person by name would receive a notification in the future notification system that a topic has been suggested for him/her to see.