LMFAO No. All moderators do is hide things. The administrators make the ultimate decisions. And it's not hard to work out why things are hidden. The posting guidelines are available on the FAQ for everyone to see http://www.girlsaskguys.com/faq/posts
Don't break the rules and your posts won't be hidden. Easy.
No, I don't see any issue with moderators being chosen by the site based off of the success rate of posts they report. If moderators ended up being chosen by users, I bet the moderation of this site would be a lot more biased.
Not that mods have all that much power, any way. Admin makes the final call.
Moderators are already chosen through having a great ratio of succes of removal. They also have the choice of not taking the "job" once asked. Their "actions" also go through the admins first, as all "removals" are sent as notifications to the admins to review. The moderators cannot do anything wrong, outside of threatening people with removal/abuse of power, in which case their mod authority is taken away by admins.
You might as well say everyone should chose Admins here, as well. Moderators get a lot of flack on GAG, but we are only the "Able Seamen" on this ship. We keep a look-out. It is Admin who are the Captains, who make the tactical decisions.
What you are asking would result in a chaotic turn-over of moderators, and a lot of fighting between members who vote different ways.
A few times in the past, they've had community votes to select mods. Usually, user reputations will speak for themselves. I can only speak for myself, but I did not apply to be mod. They invited me to join the Mod team and I accepted.