Same as above for drilling.
I've broken two mandrels for the metal bottle stoppers already, so I made my own. I got an appropriately sized bolt from HD, cut the head off and chucked it in my drill chuck. It seems that the mandrels aren't made from hardened steel.
When making stoppers from soft woods, I'll somtimes go ahead and drill it, then turn it with a drive center instead of the threaded mandrel. If you get a catch on a soft piece, it'll spin that mandrel inside the hole and ruin your threads. VERY disappointing when you're almost done with a stopper! Once you've turned the shape of it, you can thread it onto the mandrel to touch up the bottom and finish it.
I've also done some hole repair by CA gluing some kraft paper (or brown paper bag pieces) in the hole to repair / reinforce the threads. I also CA the threaded rod into the wood when assembling this type of stopper.
My bottle stopper finish is: sand to 600, micromesh to 12000, blow off with air, two coats of lacquer, two coats of friction polish.