I got my first book from PBS Saturday! I already re-posted it, but I have a question. It's a paperback with a clipped corner. I know that is within the rules of PBS. If someone requests my book, do I have to PM them and tell them?

If your book meets the PBS posting guidlines than you don't need to PM anyone.   

Nope. The only time a PM is required is on textbooks, to describe writing and underlning, or cookbooks, to describe cooking stains.

from the Help Center:

• if you post a textbook/workbook, the condition must be described to the requestor in a Personal Message
• AND the described condition MUST BE AGREED TO before the book is sent
• This is the one of the ONLY two cases in which a PM exchange about a book is required before the book can be sent(the other is for cookbooks--see below).

• No staining

  • Exception: Cookbooks may have some mild staining, since these are used in the kitchen and while cooking, and some minor degree of staining could be expected in a used cookbook.
  • HOWEVER, if you post a cookbook and it is stained, the condition must be described to the requestor in a Personal Message
  • AND the described condition MUST BE AGREED TO before the book is sent
  • This is the one of the ONLY two cases in which a PM exchange about a book is required before the book can be sent (the other is for textbooks--see above).
  • this exception applies to the covers of cookbooks also.