My Classic Turret was indexing properly from the first day I received it and put it into service. I guess I as lucky. You are right, Lee should have them properly indexed before shipment. But that would take another bit of man-hours and raise the price.
Some way of locking the thing in place after you get it adjusted would be nice. A second, lock-nut perhaps, set-screw or tangential screw. In the meantime, a product like Lock-tite might be the thing. Superglue would work (all you have to do to loosen it, I understand, is heat it up a little).
The spare black plastic thingy (Square Ratchet) is most conveniently stored on the indexing rod, just below the nut you adjusted. It is out of the way there, but easy to find if you ever need it.