I have had similar problems. I have been unable to view content requiring adobe flash for maybe 6 months, despite downloading the player maybe 15 times over that time.
One difference I have from this thread is that at the end of the download process Adobe says, congratulations you have successfully downloaded Adobe Flash Player. Then when i try and view something that requires it, I get the message that I need to update my Flash Player. I have downloaded it too many times to count. I have tried Chris Campbell's suggestions, I have tried the disk utility approach, I have tried using the offline download. The only thing I did not try is the clean uninstall, as the instructions made no sense to me.
The other different thing I see is when I go in Safari to Help, then Installed Plug-Ins nothing shows up. Its a completely blank screen. My wife's Macbook has a huge list of Installed Plug-ins...
Any suggestions would be appreciated.