We had this same problem recently and the faultbucket link pointed me in the right direction however the registry entries were different for us.
Most of our computers were fine but some had problems with Flash Plugins and some with Activex and some both.
The best way 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.
This 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
(if you copy and paste this fix remove the spaces near the end of the line added by these forums for some reason)
Reply if this solution or a similar one works for you.
What would you recommend in an enviroment of over 100 computers, some in different office, where a small percentage of automated flash deployments are failing? The above fixes dont help. Thanks