I got a book request this morning for a book that I don't have and have never had.I had the same thing happen a few months back.I went through my book shelf and the transactions and I don't have it and never did.What do you think is the problem?

I would contact PBS and give them a heads up.  There have been a couple of threads with the same question.  Unless they know about it - they can't fix it.  I just rec'd a request from an APO and the automatic DC didn't show up. 

I know that sometime when I am browsing, I end up accidently hitting the "Post This Book" button.  It happens to people a lot more than you would think. I go through my "inventory" pretty regularly to try and catch those.

I would think it would be hard to accidentally post a book to your shelf that way since you have to agree to the posting guidelines before it would show up.  It doesn't show up with just hitting the Post This Book Button. The phantom book thing happens sometimes.  Twice now I've posted a WL and had it offer it to 2 people at the same time.  I would contact PBS and let them know since it's happened to you more than once.

I frequently hit the Order This Book button by mistake and then just hit cancel on the order screen.