Now someone wants the book and I already accepted the request. But as I was getting it ready to mail out I realized it had been posted to the wrong ISBN. I received the book as a PBS swap and I didn't notice the error at the time. This book is so old, it dates from the 1940s or so and it doesn't have an ISBN at all.

So what do I do? I already accepted the request.

Can't you still click "cancel order?"  I thought you could cancel until you printed the wrapper.

Actually the sender can cancel until they click the sent button.   You do have the option to cancel, PM the member, and send them the correct (short?) ISBN so they can order it.

If it were me and I was posting an obscure wishlist book under the wrong ISBN (accidentally, as you did), I would PM the member and ask if they wanted it with the different ISBN.  I would give them a time limit to respond, and if they didn't respond by then, I would press the Cancel button.

eta: (If it hadn't been an obscure WL book, with a slim likelihood of another being posted, I would have just hit the Cancel button.)

Thanks for the input. It has been helpful.

But I was wondering if PBS has an official procedure for a situation like this?

PBS does count how many orders we cancel. But there is that little explanation box. Use it. Our accounts may get flagged by statistics, but they are reviewed by humans.

But I was wondering if PBS has an official procedure for a situation like this?

PBS's official procedure is that you must post by the correct ISBN so you should cancel the transaction. If you PM the person and they want your copy you can post it as a book without an ISBN. It is never acceptable by PBS procedure to post and send a book by an ISBN it does not bear.