There have been a few cases recently where the moderator team have taken action involving high-profile users, and that has lead to some of these high-profile users deciding to leave the site. There have also been some concerns raised about the moderation approach. I thought it would therefore be appropriate to give an overview of the way the current moderators (Martin Scharrer, Stefan Kottwitz and me) work.
The first thing to say is that almost all moderation is about 'tidying up'. I would say 90% of the flags I see are either 'Over 20 comments' or 'Not an answer' where something is really a comment. The cases I want to deal with here are toward the 'policing' end of the spectrum, and where there is something to actually make a judgement on.
The first important point is that moderation is only ever about actions on this site. Yes, the TeX community is quite compact, and there are high-profile people who the moderators know or interact with elsewhere. But any decisions to take moderator action only ever stem from what gets said on TeX-sx.
The second, related point is that moderator actions follow from cases where something looks negative, problematic for other users, or whatever. That can happen even when someone makes many positive contributions. For a 'no name' user, that's always I think clear, but when there is an issue involving someone with a high general standing, it's vital that the only thing we (moderators) look at is behaviour that has been questioned.
There is a reason my general advice if you see anything problematic is 'flag and do not respond'. That's because 'two wrongs don't make a right'. We do see cases where one user clearly is bating another. When that happens, if the second user simply flags, action is nice and clear. Life becomes much more problematic when they respond in kind: we are left seeing issues from both parties in that case.
The third important point is that we have human moderators because not everything is black and white. Some comments are easy to moderate: they are clearly offensive to someone, insulting, or just generally rude, and we can act directly. However, when it comes to questions about the content of answers, life can become more difficult. Straight-up copy-pasting is easy to address, but where there are questions about the overlap of ideas, it can become more difficult. In particular, many people are I'm sure aware that answers can get posted whilst you are writing one yourself. So a simple 'check the timestamps' approach isn't always going to yield useful information: two answers posted within minutes may well be entirely independent, in the absence of other information.
That said, we do look carefully at every flag concerning content. Irrespective of who posts material or who flags, each flag is looked at in a 'stand alone' sense: 'Is this a valid concern based on what I can see in the relevant material'.
TeX-sx is a relatively small site. We have few cases where strong moderator action is needed. That means that almost always any moderator messages or suspensions are discussed by the moderator team before acting. As such, it's very rare that only one person has looked at the evidence and tried to draw a (fair) conclusion.
When moderators take action, it's only natural that users want to know 'what is going on'. For people not directly involved, that is tricky as the moderator team cannot give full details. For example, for questions of sock puppet voting or similar, we use IP data that cannot be made public. In the case of rude comments, the entire idea of moderation is to remove them, so we can only say very general things. Where disputes involve multiple users, we have to be mindful that we have a duty to be fair to all parties involved.
Anyone who believes that there are serious flaws in the handling of a moderation case can raise this with the StackOverflow staff. They are copied in on all serious moderator actions (moderator direct messages including suspensions). The Community Management team are not involved in day-to-day decisions so are independent and able to review in a neutral way.
(All serious moderation actions send a mail to all moderators too, so for example it's impossible to suspend a user without all of the moderators seeing that it's happened.)