Comment 19 for bug 151674

Mardi,
I believe my issue with video tearing sounds _very_ similar to yours and like you suspect everyone else's is the same. I believe the problem is when compositing is enabled (and I think even when effects are disabled in compiz compositing is still enabled). To confirm try the following:

Switch to a different window manager that is not compositing enabled (such as MetaCity or KWin(for KDE3, or KDE 4 with desktop effects disabled as that does disable compositing).
Switch to xinerama for dual monitor support, again compositing should be disabled and you should find no video tearing.

Also for me I find that tearing only happens on one monitor, I have one at 1680x1050 (59.9hz) and another at 1280x1024 (60hz) and get tearing on the larger of the 2 but not the smaller (however if I disable dual monitor I don't get it on either of the monitors, which ever is enabled).
Also I don't just get the tearing with video, its more noticeable with video, but on the monitor with tearing if I shake a window around a lot for a long time with wobbly windows (and sometimes even without) you can see the tearing there too.

Finally I think it is compositing not compiz since I am using KWin-kde4 and get the tearing.