Here's a tip people, it works well before there are a lot of posts on the story. But the number of comments indicated for a story is the total number of comments. If it says 8, and you see less, that means some probably fall under your current threshold.
Crank the threshold to -1 and redisplay, then you'll get all the comments moderated down (to 0 or -1).
They don't really delete the post, but they do moderate it (sometimes it is MO staff moderating, sometimes it is users) down so that most of us don't see it. They're trying to provide a service, not just delete things they don't really want us to see.
Is there any way that I, the average user, can influence the "Score" for a particular post?
It seems like everything has a score of 1, whether it's really informative and useful or not. As stated, the really bad stuff gets moderated down to a score of 0 or -1, but, it would be nice if there was more up-scoring for the really good posts.
Would it be possible to have two scores, a moderator score and a user score? The moderator score can be used like it is now (mainly used to hide the vulgar/pointless stuff). Make the user score changeable by the average user so that it (ideally) becomes an indicator of which posts the users found worthwhile (or worthless). A given user can add or subtract 1 user score point to a given post, with new posts starting with a score of 50.
Other systems like this that I've used are configured to keep track of up-scoring and down-scoring over the life of a user, and put "status" symbols next to the user's name if they have achieved certain scoring thresholds. For example, if all of of a user's posts have been up'd a total of 120 times, and been down'd 13 times, that user has a lifetime score of 120-13=107. Since they've passed the 100-point threshold, they get a little star (or the number "107", or whatever) next to their name.
The lifetime scoring system encourages people to post useful things (so that other users will "up" their score), and discourages them from posting junk (for which others will "down" their score). If a user's lifetime score starts getting really low, you can take action (start their new posts with a lower-than-normal user score of 40, or revoke their posting priviledges altogether, or something else).