Now, aside from the fact that I'm not dedicated (I've read each of the books once and have forgotten a lot of details), I don't believe that Dumbledore necessarily knows what he's doing. (I don't think Snape is really a good guy, but that's probably another matter.)
For me, a lot of the charm of the books is that the kids are dealing with a school where they're thrown onto their own resources a lot--the adults are not reliably competent, and sometimes dangerously incompetent. This means that the kids have to use their own knowledge, judgement, and courage more than most children (or at least most of the people reading the books) have had to.
At the same time, it's a livable society--we're not talking about war refugees or (when Harry's away from the Dursley's) grossly abusive families. It's something like real life--it's possible to manage, but people are really just making things up as they go.
One piece of evidence: I made a correct guess about why Slytherin was part of Hogwarts--the founder of Slytherin was one of the founders of Hogwarts. Historical accidents can have tremendous longterm effects, and there doesn't have to be anyone's plan or intention behind them. Perhaps the interesting question is how the Slytherin lack of ethics gets moderated and/or overridden enough that Hogwartz was able to survive.
What happens to a lot of complicated theories if Dumbledore is just scrambling as fast as he can to deal with running a school (and has a severely limited pool of potential teachers--he can't just invoke sane, well qualified teachers out of nothing) and dealing with a major magical enemy at the same time?