This process is generally called preflighting, or preflight checking.
The steps include:
1) Finding PDF files
This is quite easily done programmatically, I would assume that one would copy these to a location for the preflight checks.
2) A corrupt PDF could mean a number of things depending on what you want to do wit the PDF, for instance if you're checking a PDF for printing, you would need to check colour, fonts, existance of non-support media etc. Interpretting PDF files is not a trivial task, you can use GhostScript, ITextSharp (open source) or commercial PDF libraries from Tall Components etc to performs various tests.
For a definitive result, and ability to fix files you should have a look at commercial preflighting tools, Have a look at the products from Marksware and OneVision.