Are there message boards/forums for people that run/moderate message boards?
The folks who make message board software usually have a message board for users of their software. If you run a message board that uses that software, you’ll probably want to spend some time on their message board at some point.
For example, we use vBulletin. I don’t regularly visit their forums, but I have gone there on more than one occasion to look for solutions to technical issues we’ve had here.
If you are looking for something a bit more generic, I’m not aware of anything.
One might imagine a forum where board moderators discuss spam, socks, trolls, etc etc. There would then become the meta problem of how to moderate that. 
Perhaps the board is secret and invitation only…
The first rule of Moderator Board is we don’t talk about Moderator Board…
Qui moderabunt moderatores?
To give you an actual helpful answer: Yes. The one I know best is The Admin Zone, which dates back at least a dozen years, although it might be longer. I haven’t been there in a while since I’m not as active an admin as I used to be, but it looks like it’s still pretty active.
Unfortunately, the other ones I knew seem to have faded away. Both SitePoint.com and WebHostingTalk.com had sections for Community/Forum management, but I can’t find those categories anymore.
(Actually, I can’t really deal with the new SitePoint interface at all. Frickin’ random tags instead of categories? What was wrong with grouping all topics in the same category together, for pete’s sake? Ugh, I’m so 2005!)
…But try the Admin Zone, if that’s what you’re looking for. Still seems to be relatively active.
Thank you, choie.