I'm a newbie here and am unsure if my book meets the "good condition" requirements. It is a paperback that was published with a cutout in the front cover, showing the first page through it. I guess at some point in it's life, that cutout was snagged, because a part of the cover has torn off starting from that spot. The cover is still there, there is just a piece missing that's about 3 inches long and half an inch wide.

What do you all think?

With a piece of the cover missing, no, I don't think it meets the swapping guidelines.

If it's a WL book, you can post about it on one of the threads in the Book Bazaar for damaged WL books and describe the damage.  Someone's usually still willing to pay a credit for a damaged WL book.

If it's not a WL book, you can offer it as a freebie with any order from your shelf.  Someone'd order one book and you'd send the damaged book and the book they ordered for their credit.

Hi Casey. This topic came up before a while back, and it was determined that the artwork behind the cutout is part of the cover. If it's missing, the book isn't postable. 

I want to find the post I'm thinking of, but it was so long ago I'd probably just drive myself crazy looking for it.

The page behind a cover with a cutout is considered part of the cover so the cover guidelines would apply to it. A part of the cover can be missing up to 1 square inch. Since the portion you are missing is much bigger than that, the book would be unpostable. Had the portion torn away been smaller than 1 square1 inch, the book would have been postable.

From the Help Center:

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

Welcome to PBS Casey!   Excellent question, we're glad you asked 

The answer I would have given has already been posted, thank you Melanie!

Sounds like you have your answer already, I'll just add in that the illustrated page inside the cover is often called a "stepback", in case that helps in searching the forums, or if you ever get on Jeopardy.