For those who are having this problem, here’s the fix:

1. Disable hardware acceleration

  1. Open your browser and go to YouTube.com. Start playing your video.

  2. Right click on the video and click Settings.

  3. On the flash popup, uncheck “Enable Hardware Acceleration”. Click Close.

Restart your browser and play the video in full screen mode.

Overriding GPU validation

If the above trick does not work, here’s what you can do: Open a terminal and type the following command: Start your browser and play the video in full screen. It should work now.

Other options

If you are using Firefox, you can install the FlashVideoReplacer extension. It replaces the flash player with movie player and is able to play the video in full screen and in HD quality.
via Ubuntu Forum image credit: smemon87