it's simple: follow the rules as laid out by the board owner/administrator and enforce them in the manner required by your title. inevitably, some people will be upset with you at some point, but dems da breaks. comes with the territory. it's when you start enforcing your personal opinions about subjects instead of just doing your job that a problem arises....
Absolutely, 100% correct!
Just to add my 2 cents worth to the part about "enforcing" your boards rules:
1. Your board must have rules, that are clearly written and posted in a prominent location. (don't expect people to remember what they agreed to when registering).
2. I much prefer the method of editing a post (to the point where it can remain in place); adding a comment saying what rule was broken; and then locking it. In my opinion, simply deleting a post (although sometimes necessary) doesn't help the boards community to learn.
3. If its bad enough to warrant outright deletion - its also bad enough to warrant a formal warning (provided you have a warning-leads-to-banning policy in place).
One other little thing that I've done on my board (not sure if anyone else would agree with this method, or not) is that I create a new / seperate moderator log-in for each moderator. That way, if they are participating in a lively debate or argument, which my board has a lot of, they are posting as a user - not as a moderator.
I spent time in the military, and that idea came to me as a form of being "in uniform/on-duty" vs. being "out of uniform/off-duty". In many instances the general population of my board doesn't know that the user "Joe" is the same person as the moderator "Smith". I find this leads to far fewer allegations of "abuse of power". As long as the moderators act objectively / fairly when logged in with moderator priviledges, there are few problems.
Again, it's just my 2 cents worth. But I believe that clear rules, enforced and referenced when enforcing is the key. After all, when you get a speeding ticket, the cop tells you how fast you were going, and the ticket referrs to the part of the highway traffic act that you violated. Same idea.