I just picked up a perfect copy hardcover book at the library.  The dustjacket is missing.  I checked out the title on here and it is a WL book.  But there is one other copy of the book with a different ISBN (both are hardcover).  After I read it, would I have to list it without an ISBN?  The title page has every peice of information EXCEPT the ISBN...which I have never seen happen before with a fairly new hardcover book...I assume the answer is that I have to list it without an ISBN but I hate to have this WL book sitting around forever because the ISBN must've been on the DJ...

You do have to list it without an ISBN but after you do that and have a unique ISBN for it, go to the wishlisted version and add the tag "Available under ISBN XXXXX". Someone will spot it and request it, perhaps not instantly but it could go faster than the books that roll through the WL line waiting for an active member to request it!

Can you tell which listing it is by the name of the publisher?

The ISBN must be pre-printed on the book to be posted to it so if you can't find it, then yes you will have to post it as a book without an ISBN. Look over those pages in front of the closely, sometimes they are hard to spot, but if you don't find it, please don't post it to the ISBN. Even if all the information matches and the dust jacket might have had the correct ISBN on it, there is no way to know now and there's no reason to risk being wrong and losing the credit, book, and postage money just to try to send it under the ISBN to that wisher.

It could be a book club version.  Often they are published without an ISBN.  Quite postable, though.