I have had Ubuntu running on my Dell XPS 15z for a while. I took troubleshooting to fix overheating by installing Jupiter and TLP.
Graphics errors like scrolling up by two-finger gesture opens and closes the dash quickly until it crashes, these were more of a problem I had run some command I now don't remember to activate my NVIDIA card, which since 13.04, only the Intel one works.
Recently, I installed Compiz Config Manager and enabled unity improvements and they worked flawlessly for a week. Today while playing music and switching a work space, the graphics could not keep up and it crashed. Also when I shut my laptop lid instead of locking the screen, it turned black and never returned.