I have Firefox 12 and Flash Player 11.1.x installed, and have an ATI Radeon 7000 video card.
My original problem, "Flash Player Does Not Work After Upgrade", was that the Flash Player would not work at all after upgrading to the new (11.2.x) version. Uninstalling the new version and re-installing the previous version did not resolve the problem, because the player then would just crash.
With no other intentional changes by me to the system, the Player started working yesterday. I have no idea why. I plan to follow advice from this discussion and pin the 11.1.x version so that Synaptic will not update in the future.