So I searched the bug reports to find the fix if any. Turns out to be a quick and easy fix and painless. There's actually a couple of ways you can go about fixing your Flash Player woes.
#1 Disable Compiz (Yea, I know. I'm not getting rid of my eye candy either!)
#2 Remove flashplugin-nonfree and flashplugin-installer from the Software Center. Then install directly from Adobe.com. (This didn't work for me but is reported to work for others.)
#3 (a) Open Terminal and enter:
gksudo gedit /usr/lib/nspluginwrapper/i386/linux/npviewer
(b) Then add directly before the last line of text:
export GDK_NATIVE_WINDOWS=1Fix number 3 worked for me and took less than 2 minutes. Be sure to restart your browser also. I'm not sure all of which versions of Ubuntu this is effecting or even other distributions but I'm using Ubuntu 10.04 AMD64 version.