I received a book today that weighs 4 lbs and the member used PBS postage and paid $2.47, the 1 lb. rate and it arrived, no postage due. Not complaining mind you, but I am astonished that the PO did not put postage due on it. Does this happen often?

Yes, that type of thing happens occassionaly...even books arriving without postage.  I buy counter postage, and one day my PO staff grabbed my Media Mail packages and started to toss them in the bin.  I quickly called a halt and let them know those packages didn't have postage on them yet.  With so many different options available, even the PBS 'suggested postage' notation in the upper right hand corner can look like printable postage at a quick glance.  And IME there's probably a 50/50 chance those packages would have arrived without postage due.

Sometimes it's an underpayment that gets through, sometimes it's a big postage overpayment.

Yuppers, had another PBS book arrive today without any postage whatsoever...go figure. 

sometime if its just stampls  they sometimes come off

making it look like  there were no postage

True Mark.  I mentioned the lack of postage when logging the book in, and the sender replied that he used printable postage.  Kinda made me wonder if there had been a glitch in the system during the new rate transition that reset his preferences and this one had gone through without adding postage.  Which he assumed was applied, because he always does it that way?

On the flip side, a couple days ago I received a standard size hardcover book.  IME the postage should have been somewhere between $2.90 and $3.50.  The sender had recycled a shipping envelope but not marked a rate (Media Mail, First Class, etc.) and the package had a postagl strip of $8.35...yikes!  That's expensive for one average size book, I mentioned to the sender that Media Mail rate was much cheaper.