1. The head honcho of the site is Jimbo Wales, the founder. He more or less has the final word on anything when he chooses to exercise it, but he delegates much of his authority to the next tier of site bureaucrats people below him. He also seems to stay clear of most political disputes when they don't involve him. Wales himself is a rather dubious character though - before founding Wikipedia he was an internet porn magnate who ran a site called Bomis.com, which marketed pornographic images.
2. The next tier below Wales is the wikipedia Arbitration Comittee. There are 10 members that are theoretically supposed to be elected by editors, but Wales has ensured that most of them are appointed by him. The Arbitration Committee is VERY leftist. Several of its members are high school and college kids who are typical liberal anti-war activist types, and others are old guard left wingers. Here's what can be said of some of them:
User:Neutrality - a high school student who openly professes to be a liberal progressive democrat on his profile page.
User:Jdforrester - a UK college student activist who advertises that hes "a card-carrying member of the Liberal Democrats."
User:Fred Bauder - a "retired" attorney from Colorado who is a member of the uberleftist National Lawyers Guild (note: Bauder's claimed "retirement" was actually forced when the Colorado supreme court disbarred him a few years ago for soliciting prostitution - Bauder has used his arbitrator powers to penalize and ban editors who have pointed out this fact on wikipedia)
User:Raul654 - another college student. His user profile doesn't mention his politics
User:Mindspillage - a recent college grad who advertises on her profile that she's an "agnostic atheist."
User:Fennec - another college student. His user profile doesn't indicate his politics.
User:Jayjg - don't know much about him because his profile page says very little, but his edits are well known on wikipedia to be very liberal and very partisan.
The other arbitration people are listed here http://en.wikipedia.org/wiki/Wikipedia:Arbitration_Committee#Active
3. The third tier below arbitrators is Wikipedia's administrators. These are the day to day sysop people with revert and blocking powers. There are several dozen of them and they are picked by nominations from other administrators that are then submitted for a vote of affirmation. Most of the original administrators are very liberal and this biases the election process towards them, because they seek out other liberal editors and nominate them to be administrators.
Actually, I'm exceedingly conservative in many notable respects, and also a Roman Catholic, if you find that interesting, though the full depths of my politics and views are complex (they contain both real and imaginary components, heh). Also, Mindspillage remarks of this page, "I'm a libertarian, for crying out loud."
Regarding appointments: All arbitrators were initially elected. Then some of them quit, so some were appointed to interim terms (pretty much the runners up from the election). Another election is imminent. Maybe the Arbcom suffers from some sort of left-wing volunteer bias... I dunno. Don't try to accuse Wales of subverting democracy and justice and all that, though
I'm not entirely sure that your characterization of the Arbcom as 'second-tier' is a complete representation of the picture. The Arbcom is roughly tantamount to the juducial branch - of the English Wikipedia only, mind you- not entirely like the Supreme Court per se, in that it handles more mundane cases, but it is still more... reactive than anything else. Also, it explicitly stays out of article content disputes, and engages only in user behaviour disputes.
Administrators: There are hundreds of administrators, not just dozens. Non-administrators participate in the nomination and election process for administrators in the same manner that administrators do. Administrators are generally prohibited from using administrative powers to deal with article content disputes with which they are engaged.
Finally, you left out the all-important fourth tier- general users. Don't forget them. They can't block people or protect pages, true, but they can still revert pages (with a slightly less trivial effort) and participate in all non-judicial decisions on a level equal to that of administrators.
Now, Wikipedia left-wing? The whole Internet leans a little left, in my opinion, and Wikipedia (especially at the fourth tier, which is the group which does most of the article editing) is no exception. But 'VERY left-wing'? I dunno. That's sort of pushing it. And an 'Action Alert'? Don't let's be silly, now. :) But... any steps you can take towards providing Wikipedia articles with a more neutral point of view (review our policies and documentation on that) are quite welcome, provided you conduct yourself properly and try to follow the rules and guidelines... anyway.
I'm rambling, aren't I? It's almost 2 in the morning and I really should be getting to sleep. Good night.