My AdSense rep encouraged me to set the "Sites authorized to show ads" because she has seen accounts disabled from 3rd party websites using AdSense on spam sites with the purpose of getting the AdSense account shut down. I did so and here are my observations from the first month.
There are now 84 sites listed that tried to show my ads but which couldn't. Most of them are cache sites and Google translate on various top level domains.
A few cache sites that are trying to show my ads block Googlebot via robots.txt. These sites had been causing "Robot Denied" crawler errors. I was hoping that Google would stop reporting these errors for sites that I don't claim to own. However, these sites still show up in the crawler error report.
My estimated earnings takeback was lower this month. This month my finalized earnings were 99.2% of my estimated earnings. This is better than it has been. I'm thinking that some of the estimated earnings that don't make it to finalized may be ads that show up on other sites.