I really love this question.
I have this vision of the "perfect" dominant; albeit, an unrealistic vision but at least I can admit that. In my vision (speaking VERY superficially here), my dominant is strong and dynamic. He is in good (very good) physical shape. He is very aware of his body and how to care for and maintain it. He controls himself....what he eats, drinks and how he exercises. I've gone out into the community on quite a few occasions now and I find myself being quite judgmental of those I'm meeting. Not on a friendship level, no. But if a man is introduced to me as a dominant and is slovenly kept, very overweight or just generally not in great shape, it sets off red flags for me. This man is not in control of himself.
Do I expect perfection? No. But I DO expect him to have control of his physical body. Again, I am not going into a super deep area with this and it's just my own observations. Drug use/abuse, lack of motivation, violent temper...all self-control issues and all deal-breakers.
I'm curious about what "one or two" aspects being out of control you're referring to.