I always thought that's what users were for, but now I'm told that
software should be the thing that tells me when a server isn't doing
what it's supposed to do.

It looks like there are plenty of things out there that will tell you if
your windows or linux server is alive or not - do you know of anything
that will alert you if, just for one example, your GW server (on
netware) is still running but not handling mail?