Ron wrote
My uncle gave me a "A Silver Story" a couple of years ago. ...
My question is: Should I be concerned about PVC damage ...

It sounds like a nice little presentation with the nuggets and all. I
do not know the particular set you are referring to, however. I think
I do know the _kind_ of presentation and to answer your question:
Probably not. The plastic around the coins is hard, right? Hard
plastic is not usually a problem with silver coins. The soft plastic
is. The plasticizer is PVC (poly vinyl chloride -- correcly written
as one long word) which breaks down with time, with heat, etc.

Moisture per se is not usually a problem with silver. (Your set does
have paper dollars, also.) Silver tones mostly because it reacts
primarily with sulfur in the air. You aaid that you live in the
Pacific Northwest. How's your air?

You can find a lot of information about this here on RCC, if you are
willing to do some nasty reading of long threads about "COIN HOLDERS."