I had this really weird graphical issue when I upgraded to Linux 4.4.1, on my desktop with Intel Iris Pro Graphics 6200 (I downgraded to 4.3.3, where this does not happen):

Horizontal strips of pixels (up to maybe 100px high) shift to the right (up to about 150px). It's not tearing, it notably didn't happen with video playback, but did happen on empty workspaces and ones with normal desktop programs on them.
It was always only below my mouse cursor, only on the screen that my cursor was on (I have two monitors), so moving the cursor to the bottom of the screen temporarily stopped this effect. It also sometimes disappeared completely until I moved the cursor to the other monitor.

I reproduced this in i3 (X.org) and GNOME (Wayland). I also tried to make a screencast of it, but when I played it back the effect wasn't there. I guess I would need external display recording hardware.

I'm happy to help debugging if I can.