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Just double check for any process of Safari in Activity Monitor.
You might also find that you're already using the latest version of Flash Player. Please visit this page to verify the version you have installed and compare it to our latest release.
Well, Firefox won't let me run flash player. I have 11.1 r102 installed, which firefox tells me is vulnerable.
I also checked activity monitor, and there is nothing there when I filter on the word 'Safari'.
Are you showing "All Processes" in Activity Monitor? You might want to try manually deleting the files with the word Flash in the name in your /Library/Internet Plug-ins folder then try installing again.
It turned out to be an app I have installed called "Fluid". Closing that app allowed me to update.
For me it turned out to be MenuTab Pro for Facebook. Until I quit that application during installation I got the "Safari" error.