I have 12.10 running on BBB as of today, using the images from http://elinux.org/BeagleBoardUbuntu#Canonical.2FUbuntu_Images. I also see “shaking” with my Viewsonic 1920x1080 monitor. Checking the monitor’s control panel, I see that Ubuntu starts running at 1280x920. If I use “xrandr --output HDMI-0 --mode 1280x800 -rate 60” (from memory) or a lower res., the video stabilizes. The BBB is supposed to work up to 1280x1024, but that’s not what I’m seeing. This appears to be a hardware problem on the BBB, although some monitors might work better than others.
I had tried 13.04, but it would not let me log in through the LXDE greeter.
(All is not quite perfect: I’m seeing reds and blues reversed on screen. See note elsewhere on forum.)
Hope this helps.