So if you give a thumbs down to a review does the person who posted it find out? I'm not who gave it the thumbs down but will they see that their reviews are bad?  Just wondering because I came across one today that was only posted a week or two ago and it's basically about how they won't send books they bought used to anyone with a non-smoking RC.  So will this person actually figure out that reviews aren't for personal book notes?

No, there is no way for a member to find out how many "thumbs down" their book review has received - or even if it HAS received a "thumbs down".   You can only see the number of thumbs up.

If I see that a member has made a mistake that indicates they clearly don't understand how this aspect of PBS works, then I sometimes try to contact them to let them know.  If they have a profile on PBS, that's a simple matter.  If they don't have a profile, then you have to look them up in the member directory.

I've done this several times, and each time the person who put up the review was grateful for the PM.

So it just moves them down and hopefully removes them from being seen on the book info page. But they'll still show up under the member who wrote them's reviews page.