Is there any way to see the number of copies books on your bookshelf that are in the system, other than putting everything from your bookshelf in your reminder list?

Nope, adding each book on your shelf to your reminder list is it.

No, but they should add that feature because it would be nice to see.

I've been a member since late 2005, and can tell you that this is a feature that many, many members have wished for many, many times.  But it hasn't happened.  So I'm guessing that either it's something that would be too hard to program, or PBS doesn't want to do it.   I can understand why they wouldn't be too eager to put this into place, as it would probably discourage members from posting additional copies of books that already have hundreds of copies in the system.