Ok, stakeout complete.
The mailman came, picked up the mail, and dropped it off. Inside was one of the missing Netflix disks. So. . . if someone is taking them from me, it isn't my mail man.
I think I'm just going to have to put them out RIGHT before the guy comes, and pick up my mail right after it's picked up. Can't give anyone a chance to go shopping. If that doesn't work then a P.O. Box it will be--it's right down the street.