To answer Pete's question:
Anonymity would shield moderators from the off-site wrath of the more troubled users with whom it is their special privilege to interact (and some others who are onlookers). Moderators are much more exposed to such problems than regular users and do not have as much choice about their level of exposure.
From my regular-user experience here as well as other Internet (and real-life) experience with relevant populations, I can attest that quite a few of the "problem children" one might encounter through a site like this are highly intelligent, manipulative, sociopathic, narcissistic etc -- usually in an interesting combination. Some have the programming skills to mount denial-of-service attacks on identifiable websites connected to moderators, or the investigative cleverness to track down physical addresses, phone numbers and so on should they wish to operate offline. Many seem to have a large supply of spare time.
If anything I would urge SE, especially as the site grows, to anonymize the moderators after election rather than making them more identifiable. Thus, if "Joe X" is elected as moderator, he can continue to use the site in a non-moderator capacity as Joe X, but all moderator functions such as deletions, closures, contact with users, etc are performed as "Moderator #23" or as "Math.SE Moderator" without individuating Joe at all. On the other hand, moderator actions should be made as visible as possible, with publicly readable logs.