I received a book in the mail that I requested from another member. The front and back cover have some pretty significant worn bends in the cover and the very center pages of the book literally fell out when we opened up the book for the first time, they are not connected to the book at all. Is this okay? Or do I ask for my credit back?

Yes, the book is RWAP if it arrived with pages falling out.  From PBS Help Documents, Swappability:

Pages:

• No torn or chewed/gnawed pages
  • yes, that does say "chewed/gnawed".  That means no pet-chewed (or human-chewed) books.
• No loose or missing text pages
  • for travel guide books - maps if designed to be detachable may be detached, but must be included.
• Cover not water damaged (there may be no water damage to any part of the book)
• No writing or highlighting or underlining on text pages

The bends on front and back cover are somewhat discretionary.  Although bends and creases on the cover do not in themselves make the book unpostable, at some point the book ceases to be 'in good condition' and becomes 'excessively worn.'  If the bends are such that the cover is torn, that is also covered in PBS guidelines:

Cover:

• Must both be present (front and back)
  • note that a paperback missing its front cover is  usually an illegal, unsold copy
  • "cover" does not = dust jacket.  Hardcovers do not need to include their dust jackets to be swapped here.
• Cover not water damaged (there may be no water damage to any part of the book)
• Cover not torn or chewed/gnawed
  • some used book stores cut out a small part of the cover; if the amount missing is less than 1 square inch, this is OKAY
  • a small rip (less than 1 inch) in the cover is OKAY
  • yes, that does say "chewed/gnawed" above.  That means no pet-chewed (or human-chewed) books.
• A bookplate inside the cover or on the flyleaf is OKAY

If the bends look fresh, it might be shipping damage. But "worn" makes it sound like they're aged. Like Denise L. said is subjective unless obvious/extreme.

As far as the center pages, these are sometimes picture/image pages, especially in biographies. So, what about if they are not text pages or maps?

With all of the cold recently, I wouldn't be surprised if the glue got frozen/brittle and snapped.  The book might have been postable when mailed, but transit might have been the last straw.

It is a childrens book that is completly held together with staples for the binding, and the pages were not attatched to the staples at all, and you can tell that it is old and has been that way before shipping...

Loose pages are always unacceptable. Pages need to be attached to the binding. There is only 1 exception to this ... for "non-text" pages.

There is no exact definition of what a "text" page is vs. a non-text page ... but non-text pages generally refers to ancillary pages in the book ... book review pages, publisher pages of book advertising, blank pages, basically that stuff at the beginning and end of the book that the publisher sticks in, and the author or editor did not write.

So, pictures from the middle of the book are definitely text pages. They are part of the text of the book.

Coupon cards to order books from the publisher (that might also be in the middle of a book) are not text pages.

As far as bends in the cover goes ... that's in the eye of the beholder. It's not against the rules, but if there were "tons" then it might make the book not "in generally good condition" bu thtat's a lot more subjective.