What exactly is the issue? it seems to me that there isnt so much a perceived problem in the power of the mod (I can delete posts after all), but more of an availability issue. Ie when I am abroad I can't moderate the 1.e4.. section. So maybe it is an idea to make a mod chiefly responsible for his own site but give him the same powers in other sections. That way spam can be quickly deleted whenever a mod sees it.

Me personally I have had to delete a post only twice in the 1.e4.. section, iirc they were some sort of weirdly generated posts, so the issue is not that big I think. Though to be honest when people are trying to revive the Alekhine I sometimes do get tempted... 

I'm surprised that there isn't any filter activated that would disable a poster for using so many keywords typical of spam messages. Is that not possible in a YaBB forum?

I know that the sections that I moderate have been hit by spammers in the past, but this is the worst I've seen.   

The situation isn't as bad as it seems, since most sections have very active moderators.  I don't think moderators need more power, but it's clear that we do need a back-up moderator in the Chess Publishing General section.

Has spam been a problem?  I'm not aware of it.  If someone wants to cure a specific problem, they should point to an example.   

Anyway you have disagreements among moderators as to what should be deleted.  I'm not sure that's a bad thing.

There is no overall statement of policy, which may not be a bad thing either.  A little common sense goes a long way.

First of all, the situation we have at the moment is untenable, imho. Ok, the spam threads are "only" irritating and so far limited to only one section, but it could even be worse with things such as abuse and what not. But it's simply idiotic that we can have someone wrecking the forum for hours on end. So, yes, it would be highly welcome to have more members having the power to help in such situation. Whether it should be extended to all mods, or only a handful of the most trusted (and of course active) members depends on the selection process of the mods. 
While scanning through almost all of the threads I came across the thread in which the mods were appointed and it just seemed to me that the process was, errm, rather short. Mind, I'm not implying that any of the current mods are not doing their job properly, I just wanted to point out that - theoretically - Mods with more powers could do even more damage than a spammer.

In conclusion: Yes, we need more people to limit the damage, but it makes the Mods and consequently their selection even more important.