The last one I can remember who pissed off about this was nutildah, who seems to have left the forum for good as a result.
I am not aware of any case in which nutildah had any action taken against him for *arbitrary* reasons.
To answer your question, every mod implements the various forum rules and policies a little differently, however, I have never had moderator action taken against me, while acting as a moderator, which similar action was not taken against others in a similar situation. There is one moderator who is not good with keeping confidential information confidential, however, I would not say this particular moderator takes actions that he does not implement for others (that I am aware of).
Unfortunately, I have encountered instances in which some reports of mine were either not acted upon, or marked as "bad", likely because some moderators were not able to immediately independently verify the information, even though the information is available to the admins (and possibly some of the moderators). This is unfortunate because it has resulted in hundreds of reports of mine being marked as "bad", even though the reports were accurately reporting a post violating the rules.