Firefox not detecting Flash 11

You appear to have installed the 32 bit version of Ubuntu. You might want to see if you have flash installed directly in your profile:

find ~/.mozilla -name *flashplayer*.so

If you do, you might want to note where it is and move it out of the way (while Firefox is closed). Then, reinstall the version from Software Center.

I had the exact problem with me.

This is how I fixed it:

Open up terminal and type:

 sudo apt-get install synaptic

After that run synaptic, by searching for it on the home dash, then type in the search field flash. In the results right click on adobe-flashplugin package and select mark for installation. It should also select a properties file for you automatically. Then click the apply button and go on. When it has finished the installation you should have Flash Player.

Fixed it!

While running Synaptic (as I was lead to by 11chubby11 - many thanks) I discovered another plugin, gnash, and decided to remove it.

When I started up Firefox, YouTube couldn't play videos at all (whereas before they WERE playing, just with poor quality). This lead me to suspect that Firefox had been using Gnash as its default plugin. So I went back to Synaptic, found adobe-flashplugin, marked it for re-installation, and applied. Voila, my video now works beautifully on YouTube, and even better, I was able to use Vimeo for the first time on Ubuntu. :)

Thank you both for your help.