I have a book called "Songs of a Humpback Whale" by Jodi Picoult.  It   has the ISBN:  0743431014.  The info that comes up for that ISBN is here:  http://www.paperbackswap.com/Songs-Humpback-Whale-Jodi-Picoult/book/0743431014/ .  But the book that comes up says publication date  is 2001.  Mine is 1992.  Can I post it as the one that came up or do I make a new listing?  If I do make a new listing, will it accept another book with the same ISBN?

Only title, author, isbn and binding have to match. Cover picture and publication year do not have to match and there is no need to ask the requester if an older publication date is acceptable. 

FYI...You can't create another book with the same ISBN. Or any other ISBN.

You can only create listings for books without an ISBN and the system will assign it a random 6 digit number of it's own.

(Sorry, I use the word random as in not related to being issued by the publisher/author or in any way related to the book anywhere other than for PBS's own use.)

Books that have been been reissued by the same publisher often have the same ISBN. The 1992 date is simply reflects an earlier edition or printing of the same book.  It can also go the other way, as you may find books in the database listed with an earlier publication date than the copy you want to post. As long as the title, author, ISBN, and binding type match the listing in the database you can post the book; the publication date and publisher information do not need to match your copy.

"You can only create listings for books without an ISBN and the system will assign it a random 5 digit number of it's own."

This statement is not correct. The system does not assign a random number to books posted without using an ISBN. PBS assigns numbers sequentially to books posted without ISBNs. Currently the assigned numbers are only midway through the 6-digits, with the most recent number being around 44998x or so.

If the most recent short ISBN number is 449985, for example, then the next book posted by any member without an ISBN will be assigned 449986, and the next one after that will be 449987, etc.  These are assigned sequentially, not randomly.

The thing that is crucial to understand is that every book in the system must be identified either with a unique true ISBN-10 or ISBN-13 assigned by a publisher, or with a unique "short" ISBN assigned by PBS.

As already posted, only the ISBN, title, author, and binding must match.  Unless specified in an RC, cover pic and publication date need not match to be posted.