I looked at the PRV today and noticed some white corrosion on the top, like corrosion on a car battery would have. Would this have anything to do with it? It started happening this fall when it got cold. The vibrating is in the wall of the room close to under where the main floor bathroom is. Daylight basement home.

I would assume that the "white corrosion" is a build up of mineral deposits around a leaking adjustment screw of the PRV. That would indicate a build up of mineral deposits inside the valve is possible and may be the cause of the vibration. I would replace.
However, if the vibration only occurs when the shower is used, it may be caused by a loose washer in the shower valve.

Agree with Harold: the vibration is most-likely caused by loose washer in your shower valve. Sometimes it can also be loose stem and/or pressure balancing device. If it is washer than it is easy fix: turn off water, remove stem, replace washer, reinstall stem and turn water back on. If it is loose stem, then you may want to get new one. If it is loose pressure balancing device than get new cartridge as well. That should do... Milo