We use the MSI versions and have had this problem. Adobe needs to fix their MSIs.
I figured out the solution recently from reading Adobe forums and doing some testing.
Most of our computers were fine but some had problems with Flash Plugins and some with Activex and some both.
The best way I found to fix a computer or set of computers is to first uninstall all Flash and then note all remaining Flash entries in HKEY_CLASSES_ROOT\Installer\Products.
These entries can vary based on what versions got corrupted on your systems.
What I pasted below ended up being the fix for us for both Flash Plugin and ActiveX version. We tested it and had great success as a .reg file and are now deploying it via GPO.
(We had 4 defunct registry entries for Flash plugin and 3 for Activex)
Windows Registry Editor Version 5.00
[-HKEY_CLASSES_ROOT\Installer\Products\371245C90F69D5349AC564C8AA7CE50A]
[-HKEY_CLASSES_ROOT\Installer\Products\6205276E056AC94498B76D7B5AEE0A85]
[-HKEY_CLASSES_ROOT\Installer\Products\6F8CE5C1F5C5F12458EB19B9D5C0DAC4]
[-HKEY_CLASSES_ROOT\Installer\Products\FB0D7F53BA803E244A30FA7927CA12A6]
[-HKEY_CLASSES_ROOT\Installer\Products\30D9D84132D5F4D45B0DAB06034CD5FC]
[-HKEY_CLASSES_ROOT\Installer\Products\C460100B160DEAB4091314A638D85563]
[-HKEY_CLASSES_ROOT\Installer\Products\4E867BFF724E3554CB631AF1E5269AD4]
(if you copy and paste this remove the spaces added to the middle of the lines which the forum does for some reason)
