To me, the two key factors to consider when judging the worthiness of a person's position (when you don't have the time or expertise to go to the original data) are
1) COMPETENCE = training + education + experience + skill + demonstration of the ability to apply them, and
2) MOTIVATION (be it money, power, glory, altruism, grades, friendship, or passing your genes on the next generation)
No one person can be competent and motivated in every topic. You NEED to put some degree of trust in the statements of others if you are going to get anywhere in the world. (And even distrusting the statements of people you find untrustworthy provides information. For example, I tend to distrust Rush Limbaugh. Occasionally he is right, but generally when he says something, I automatically start looking for the flaws!)
It would be possible to come up with some sort of ranking matrix, but that is almost certainly overkill, mostly because many of these are subjective, and because they change. But a rough assessment for various situations is possible. This doesn't mean the answer is right, of course, but it does mean it is more worthy of consideration.
So when John Denker gives an opinion on physics i tend to trust it, because I view him as competent and motivated.
When John Denker gives an opinion on medicine, I know that is not his area of training, but as a scientist, he has broad abilities to understand problems. He is also highly motivated by friendship, which means he is less likely to gloss over things and more likely to dig deeper. I don't trust his medical opinions as much as I trust his physics opinions, but in the cases he mentioned, his opinion is definitely worth considering.
A 10 year old doing a science project may be motivated, but lacks many of the areas of competence. I would not tend to trust that opinion - instead double-checking the results myself more closely.
Paul Wolfowitz has training, education, and experience. To President Bush, he may have demonstrated appropriate competence, but I seem to have a different opinion. Motivation is subjective. Motivation by right-wing political ideology is a positive point to some and a negative point to others.
PATTERNS of competence and motivation are also important. When several Presidential advisors are shown to have poor judgement, then that calls into question the competency of the person who chose them. This in turn calls into question the competencies of peers.
This is where scientist are vulnerable. When anyone claiming to be a scientist mis-steps, it tend to lower the trustworthiness of ALL scientists by association.
There is a whole lot more I could say, but other duties call ...