I ended up going out on a service call to a client's theatre this afternoon to troubleshoot some "humming" on their intercom system. It was an interesting enough solution, with both some fairly common and unusual aspects to it, so I thought I'd post it here for everybody's benefit.
So, here's the setup. They've got a simple single channel intercom system, with a power supply station (in this case a Production Intercom PS-2, although this could equally as well have been a ClearCom system, since the systems are interchangeably compatible). Three single-channel beltpacks are chained on the first channel of the power supply, and the other two channels are unused.
The client was reporting "buzz" in the system, any time they tried to use it unless a mic was keyed. If the stage manager turned her mic on, the buzz went away, but only at a very specific (and too low) volume setting on her beltpack, turning it up loud enough so she could hear anything resulted in what she described as a "squeal".
When I listened, the "buzz" sounded like a fairly low pitched hum, but higher in pitch than ground hum. The "squeal" was still a hum, but noticeably higher in pitch (maybe around 200 Hz).
The power supply metered out both proper voltage (24V between pins 1 and 2) and termination (4kOhm between 1 and 3).
There was one other symptom that I noticed in testing, but that the client did not notice, and would not in their usage of the power supply station, but that did help in narrowing down the problem. If nobody comes up with it in the next day or so, I'll post it, but in the meantime, see if you can either solve the problem without it, or at least start down the road on troubleshooting it and find this symptom on your own. Feel free to ask things like what happens when you turn X on, push button Y, jiggle cables, etc and I'll post back.