Qualifications for Overseers (v. 1-7)
There was a footnote in my bible that says overseer is something like a bishop, so we are talking about someone overseeing matters of the church.
Overseer is a noble position, so those who seek it must be above reproach. He should be the husband of one wife, sober-minded, self-controlled, respectable, hospitable, able to teach, not a drunkard, not violet but gentle, not quarrelsome, not a lover of money.
The interesting item in this list is husband of one wife, this seems to imply that other people in the church can have multiple wives. I suppose you could argue that this is saying he can't be a bachelor, but then why not say "a husband" rather than specifying "one wife"? (I was going to put this in the bad section, but then I realized that as long as everyone consents, I don't have a problem with polyamory)
He must manage his household well, keeping his children submissive. For if he can't manage that how can he manage the church?
It makes sense that you need to have you own shit together before taking on a big responsibility, but why is the measure of that having your kids be submissive? Having your kids listen to you is important, but it seems to be the only measure of good parenting that comes up in the bible. (Colossians 3, Ephesians 6)
He must not be a new member to the church and he must be well thought of by outsiders, otherwise he might fall into disgrace, or a snare of the devil.
I suppose the snare of the devil could easily enough be interpreted as metaphor or something. The rest here seems reasonable.
Qualifications for Deacons (v. 8-13)
Similar rules as for the Overseer but the qualifications seem a touch lower. Example, "not addicted to too much wine", and "not greedy for dishonest gain" as opposed to "not a lover of money" for the overseer. But basically the same idea, he needs to be an upstanding guy with one wife.
There was one interesting thing though, v9 "they must hold the mystery of faith with a clear conscience" What is the mystery of faith? The phrasing just seems weird to me.
The Mystery of Godliness (v. 14-16)
Paul says he's writing this in case he is later than he intends, Timothy will know how to act in the church. He then says that the mystery of godliness is that God was manifest in flesh, vindicated by the spirit, seen by angels, proclaimed among the nations, believed on the world, taken up in glory.
I think the real mystery is what the hell Paul is talking about.
For the overview post (If you think I should add or remove stuff from this list please let me know, I think it would make good conversation)
3:2 implies that bigamy [-edit thanks TWF- or perhaps divorce] is acceptable (or at least tolerated) among the rank and file of the church
"Therefore an overseer must be above reproach, the husband of one wife, sober-minded, self-controlled, respectable, hospitable, able to teach"