Hmm, so your getting bad video playback fullscreen using an onboard Intel GPU. Maybe yor using something like Atom Processor D4xx/D5xx/N4xx/N5xx Integrated Graphics Controller?
you might need to install hwinfo, it is in the repo
sudo apt-get install hwinfo
Get the Intel Linux drivers from the official Intel open source drivers center here
Follow the instructions on that page, especially the part about the signatures.
once installed, and rebooted, try adding the line
Option "TearFree" "true"
to your /etc/X11/xorg.conf file and reboot.
If your still having playback issues, then that will be due to the default video player ‘Video’ (totem).
sudo apt-get install mplayer smplayer
Right click your video and ‘Open with’ smplayer.
now enjoy smooth full screen video playback.
Some people prefer VLC.
Also of note is the GPU’s I mention above do not have any hardware video decoding so might still struggle with full on HD video. There’s nothing you can really do about that.
Please do leave a comment if you find a better solution, or this works for you on different hardware.