One of my servers is kind of old, and sometimes it takes a while to
establish communications with some of the others. How can I check on the
state of this, e.g., right now, after restarting the old server, it can't
communicate with one of the three others, each of which can see each other
just fine. This will fix itself eventually, and I can already PING both
ways across the problem connection.

I just installed SP6 and the post SP6 updates on the old server, which is
why I'm slightly concerned - installed SP6, rebooted, installed the post SP
stuff, rebooted again.