You want to stay away from 13 for a while anyway. Believe me.
Follow those steps to reinstall 12 if necessary, otherwise wait a week or two till they get the bugs worked out of the Mac plug-in.
From your linked article:
"Flash Player now attempts to use CPU instructions that are not available on a subset of supported Mac hardware from 2006 to 2007. "
Since, as I stated above, I have a 2012 iMac, I'm not affected by this bug. Also, I'm not having "plugin failure" as that implies the plugin installed successfully and then failed during operation.
The problem I was having is that the installer program was failing the install process, giving no reason why, and Adobe's troubleshooting sites to which the installer links are abject garbage.
For the record, after a restart the installer completed successfully. I have a feeling that there was a memory issue somewhere or a process that was running which it didn't like.
Still no reason to have such uninformative installer information, and such completely unhelpful troubleshooting pages though.
Just another reason I don't use the GUI installer, and choose the offline installer. It's a few seconds longer to install than if the GUI installer works properly, but it ALWAYS works, where the GUI doesn't.