Adobe Flash Player 13 failed to register on Windows 7. Why?
I also had the same 'Failed to Register' problem with Flash Player 12 update install. Was only able to recover by doing a system restore which stopped it asking me to update and then failing. I didn't try to update after the system restore so don't know what is on my machine now.
I've downloaded the cleanup from adobe and ran the program as administrator and nothing worked. I even deleted a registry entry which also had no effect.