Automated PDF file integrity checking?

WomensHealth writes: "I have about 6500 pdfs in my "My Paperport Documents" folder that I've created over the years. As with all valuable data, I maintain off-site backups. Occasionally, when accessing a very old folder, I'll find one or two corrupted files. I would like to incorporate into my backup routine, a way of verifying the integrity of each file, so that I can immediately identify and replace with a backed-up version, any that might become corrupted. I'm not talking about verifying the integrity of the backup as a whole, instead, I want to periodically check the integrity of each individual PDF in the collection. Any way to do this in an automated fashion? I could use either an XP or OS X solution. I could even boot a Linux distro if required."