Yeah, I should point out I'm not behind this karma thing, but talking about it should come up with lots of interesting stuff at least, and might lead to a simpler system, and I'd really like to see something we can reasonably fit into 0.2.8 to give some relief now.
You bring up an interesting possibility I hadn't even considered, z-man, that the system should allow quite nicely. Players asking the server for a moderator and the server picks one randomly and assigns him to fix the problem.
I was thinking that certain actions shouldn't be tied into the karma system. Having vote polls tie into the karma system would probably be nice, but ingame admin actions shouldn't. I don't think the system should give admins any sort of advantage, I could set up a server and call it something like "Titties and beer", which would immediately get half the community in there to see it, and kick everyone. Now I've lured everyone into a karma trap. We could have polls for rewarding players by gifting their karma, though, for when someone does something exceptional.
I think one of the keys is in metamoderation. It would be possible for me to setup a server, get all my cronies in there, and go through a series of polls gifting ourselves until we're gods, and then go trash the world. So servers have to be subject to karma on their own, and players need to be able to metamoderate the servers themselves.
So you bring up the idea of having the system local to a server, and I'm thinking that should not only be possible, but it should be opt-in anyway, like anything else. Karma has no effect on your server by default, although it is tracked, and you have to enable it to get any use out of it, then you have to enable it to tie into any sort of global network. It would be nice if it were possible for folks to subdivide, so when someone winds up with a community that really dislikes ours and doesn't want to participate here, they should be able to set up the system for themselves, and we can then metamoderate them amongst ourselves (without giving them a global penalty, of course), and they can do the same right back at us. I wouldn't like to see this happen, but I'd like people to be able to do it.
Ok, that's what I thought up reading your post, now to specific points.
@behaving differently on different servers
I consider this a problem to be solved. Think of it like the old "you're always nice to me when he's here, but when he's not here you're a dick to me". A large network that everyone's more or less tied into would allow a community standard to evolve that would see enforcement of sorts everywhere, obviously stronger on some servers than on others. I think that would be a Good Thing.

Obviously it should be configurable enough to a server admin that he can pick and choose the parts he wants so his server will run the way he wants it, and he can get benefits from the system even if he doesn't use all of it. That's where it's possible for people to behave differently, they might take a karma penalty on other servers, but you expect that when you go to the red light district.
It might be useful to just collect karma values from servers and not keep a master value anywhere, and to cut the forums into it we'd just setup the forums with their own karma server. That way when I metamoderate some dumb clan server for myself, I can also see karma ratings for players that play there and have their own karma ratings. For example, I hate clan FUK, those guys are jerks, and I figure I want any of those players to see a karma penalty that's inversely proportional to their karma on the FUK server. That at least gives us a distributed system....
@moderator tasks
I was personally thinking moderators can only give karma to people and take it away, but they can give more than they can take. So it's easier to reward people than to penalize them. Unless you want a karma mode of 0, or at least a median near 0. And also certain things should never be affected by karma, like vote-kicking. Even now we see without a real karma system the problem, and karma would exacerbate it. A good example was somewhere around 6-8 months ago, I was on Swampland and behaving like an ass (yes, even I misbehave sometimes). The poor victim of my behavior tried to kick me, but *couldn't* because with a certain set of players I am virtually unkickable. And I have to say I'm flattered by this, but somewhat disappointed. Karma should never make it impossible to take action against a player. Maybe it could raise the bar against certain players. Like FUK shouldn't be able to fill up a server with their players and kick someone they hate and then leave. I would probably be against karma giving someone any kind of bonus or penalty in polls. I like the idea of asking the server for a moderator to resolve a problem and the server picks based on its own metamoderation scheme and stuff, but maybe we should consider that all he can do is kick a player without penalty, if that.
I would rather see a server admin use metamoderation to give moderators privileges. So I could metamoderate my own server to give Lobsters and Swamplanders bonuses, and then say "anybody with a karma of 30 can kick/silence players", and as long as Lobsters and Swamplanders keep their own servers pretty clean, my server will benefit from this. I could also make the FUK guys into virtual pariahs on my server and only my server.
@ playing while moderating
Depends on what 'moderating' winds up being. I don't really have an answer other than acknowledging that the usefulness of the system decreases dramatically if you can't moderate while playing.
@ balancing
I don't really have an answer.

I've been trying to figure out what the function should look like, and trying to avoid the bell curve. I was thinking about using a decay system like the ladder already has, but a tad better (decaying at other times besides when the server restarts

). That would require players to make regular contributions, so you couldn't just save up a bunch of karma and become a god. I think that if people are more likely to punish than reward, we could find some balance by making it harder to punish than reward.
I'm pretty stumped on how to balance it.

There are probably lots of ways to work the algorithm, but we probably need to know what the function looks like before we know how to force it to the shape we want, and then we have to determine the best shape to force it into.