I am a retired forum Admin veteran, I used to manage many boards from small scale board of a few hundred members, to a few boards with a few hundred thousand back when i was perhaps 16-21. One of my biggest passions was forums and how amazing they were at bringing people together. I ran many successful forums in my foruming prime, and i've seen it all when it comes to members wanting to become staff and the sort.
With regards to what i used to look for, i only had 4 things i really cared about the most, the others could be learned:
Trust: My top priority on any list, moreover mutual trust, would that mod trust me to do the right thing for the forum by promoting them or dealing with any problems they encountered, would they trust me to teach them if they were unsure of anything and take the time to teach them? Also could i trust them to respect the other members, not let the power go to their head and to do the best job they could?
Loyalty: A similar thing to trust, loyalty to me means having that dedication and commitment to the end goal of the forum and its owner/Admins, i'd want a person to want to share in the forums success and work together with the team to build and nurture the forums growth, to put the effort in and have the passion to want the forum and themselves to succeed.
Respect: This is one i'm a big believer in, if you cannot respect the rules or your team and your members, you're not going to do well as a Mod, a good Mod respects his/her peers no matter what level on the chain they are, if they respect others, they will not only build rapport, but also mutual respect. after all if you yourself respect the rules and role model them, others will look up to you and follow in your footsteps.
Honesty: Again similar to trust and loyalty (notice how they all link nicely together), Honesty is a MASSIVE part of my philosophy, if you are not honest, you cannot be the other three things on my list, honesty breeds success and if you're honest with your team, your members and others, you will always do well, it's ok to make mistakes, its ok to miss judge a situation or do something wrong, but it takes a great person to admit they are wrong. With honesty you can work together to fix an issue, or work on a solution to solve a problem. Without honesty, no matter if you think you have the other 3 traits, you don't. Honesty builds respect, which in turn builds loyalty which then builds trust.
If you have all 4 of these in a person, you'll always choose a winner, anything else such as good grammar, knowledge and capability can be developed through helping each other.
I live by these 4 principles and any great forum will thrive one these. That is why i enjoy coming here, the community here accepts others, there isn't any dis-respect or complaining or being mistreated (that i've seen).
If we see a member doing something wrong, we don't bash them or make them feel crappy because they made a mistake, we point out the mistake and help them learn from it to become better. The same goes for Mods here, i'm sure i've seen instances where a Mod has perhaps mistaken something, and we've pointed it out to them in a way that wasn't derogatory to help them (mutual respect).
Additional things i'd tend to look for after the big 4 would be
Knowledge of vBulletin, experience always helps, having someone who knows how to code is always a bonus, but again this can be taught.
Passion, there's no point being a robot about something, a good leader always has passion in what he/she does and has fun doing it! this also rubs off on your members :)