I would say that forum admins take leadership roles - where the members look up to the moderators, the mods look up to the admin as well.
And just as moderators need to be the objective voice amongst members (ie, to calm down arguements and such) it can be necessary for admin to lay down the law amongst moderators as well.
I run a guild in an online game, and as a forum admin also, I see many comparisons between the problems that can occur in both.
Clans / guilds in games hold the same heirarchy and are generally formed under one purpose or ethos. Allowing factions to rise within that community can cause it to split - that's where officers (mods) come in to moderate members and leaders (admin) come in to moderate the officers.
(TIP: Ive learned soooo much about online communities from gaming it's unreal (pardon the pun) - I can spot a troll a mile off these days!)
Online gaming communities are perhaps a more extreme example of how other online communities could be (more competitive = more arguements), but can serve well as an example of (virtual) human behaviour.
After a while in a community, you can spot the same types of people - those who constantly push for change, the diplomats, the trolls, the leaders, those with self-interest only, the newbies, the seasoned posters.......
As a forum admin, you need to learn to spot these groups and more - that's the best way you can prepare for potential problems.
You also need an eye for detail - on my regular (non gaming) forums, I have in past been able to "out" a competitor causing trouble simply by recognising his post style. Left unattended (or even simply given the benefit of the doubt), he could have caused problems for us down the line.
This skill helps with subtle spammers as well. ;)
But the best skill a forum admin can develop is to learn where to drawn the line. Sometimes it's better to ignore a flammer than let the discussion carry on for ages. There's nothing more satisfying than ripping it out of flammers, but most of the time, it isn't best for the forum. Although, laying down the law in no uncertain terms can be equally effective at times! ;)
You need to be able to let go as well - I was very obsessive about my main forum when it started - too much control will just drain your will! :)
Running a community is very much a full time commitiment - especially if you are starting out with noone to take some of the responsibility.
Ive seen forums chucked up and left alone after a while - and they just die - yeh, there are posts, but no discussions, which kinda defeats the purpose! I get the impression that some people use forum software as an easy way to maintain an information site and just hope the community will take off! Not gonna work!
A forum is like a garden - it is as good as you want to make it and it can be left for a while, but does need maintained and occaisonally the neighbours dog gets through the fence and takes a..... ;)