"It seems somewhat random and broadband, so perhaps it is not city QRM? "
The composite noise of everyone's computer, TV, etc can just be a pretty steady noise floor with random bursts when something particular loud cuts in.
Natural background noise sounds the same as it did six years ago, on average. If it doesn't sound like natural static-crashy background noise, it's probably manmade.
" But it might be noisy. I have no idea what it is hooked to. When I ground to the cold water pipe, the noise increases noticeably without much signal increase. So the cold water pipe is noisy.
That was my experience operating from an apartment... the balcony railing was noisy :-) I used magnet wire out to a tree fed against the railing.
I finally got around the problem by shooting another random wire out to another tree and feeding the two as a random doublet with a remote tuner at the feedpoint.
That knocked my manmade noise level down quite a bit, and I was pretty happy with the results for the next couple years...
Basically, fully balanced antennas completely choked off from a building electrical system helped a lot in my situation.
If you're happy with the transmitting performance of what you've got, and just need to hear better, you might try a small receiving loop (with an inductive coupling loop, not a gamma match)http://www.n3ox.net/projects/rxloop
or a small version of a terminated receiving antenna like a flag or pennant http://www.n3ox.net/projects/flag
Even a small dipole with an isolation transformer might help.
It never occurred to me to install receiving antennas (besides the RX loop for 80m, which I later found I didn't need) in my apartment, but I think it could have helped.
That said, make sure your own nose is clean, so to speak. I didn't really need the RX loop is because the horrible S9 noise I was getting on 80m (which was rather broadband) turned out to be my own computer. I finally put two and two together when I discovered that the null direction was changing substantially when I moved the loop to different parts of the living room.
I accidentally triangulated it ;-)