Mmm.. turning off the overhead work lamp makes a noticeable difference -- it seems to account for perhaps half the noise I'm seeing on some things.

Still seems excessive to me, but what do I know?

Now I've got a 5.6VDC battery pack -- four NiMH cells in series. Aligator ground clip on one end, probe tip on the other. On the 1V/div scale, it shows a noise level of 456mV on the *DC* signal.

Which is pretty much the same noise floor it "sees" without anything connected to the probe inputs.

So now I'll skip the battery, unplug all probe leads, and just let the scope measure ambient noise with no leads plugged in, and the input set to 1:1:

Peak-to-Peak measurements of the "signal"

625-625mV at 5V/div.
667-833mV at 2V/div.
458-500mV at 1V/div.
*click*
62.5-62.5mV at 500mV/div.
66.7-83.3mV at 200mV/div.
41.7-54.2mV at 100mV/div.
*click*
6.25-8.33mV at 50mV/div.
6.67-8.33mV at 20mV/div.
5.00-7.08mV at 10mV/div.

I wonder if all of this is due to the simple plastic case that this thing is wrapped in?

Meanwhile, confirmation of my observation as to which mV/div settings exhibit the lowest noise:
The first bit about the VGA is irrelevant. But I wonder if a Tek TDS2000 really is this noisy. Anyone got one? Connect a AA battery to it, and check the noise level at 500mV/div.

??