Ok, I'm back.
My experiments with the radio didn't turn out so well. I hear a distinct hum on any empty AM frequencies on all the radios that are plugged into the wall. I'm resonably sure that it's from the line because I've heard that same hum from things that I know are produced by the line. My battery powered radio doesn't have the same hum, but there is something there. However, it doesn't show up on all frequencies, just the lower ones, ~<750kHz. The other problem is that everything that runs on electricity produces some kind of noise if I bring the radio close enough. I can hear my computer think. There's also all sorts of cool noises at work.
Back on the oscilloscope, however, things have changed. For some reason, I can't reproduce what I had before. But, while I was in there, I decided to take a look at the line. It's definately a sine, but there's some irregularities on the falling side (going toward 0V) of each peak. It looks symetrical, so whatever is introducing the noise is only happening at a certain voltage (positive and negative).
I added more pictures to the same page:
http://ratlab.dyndns.org/scope/1/
Any more insights before I turn off the power room by room to eliminate an internal source?