For a while (possiblyprobably since I installed it) I've had weird graphical glitches on resuming my laptop from deep sleep. Until now I'd settled for rebooting it to fix it but I went on the hunt for a better solution.

This seems to be a common problem with the Intel graphics drivers and Linux - I found numerous pages from lots of distributions (including Ubuntu, Arch and Fedora) describing the same symptoms.

I did, eventually, find a suggested soltion which is to switch the Intel driver from the newer SNA (Sandybridge's New Acceleration) to the UXA (UMA Acceleration Architecture). I did this by creating a /etc/X11/xorg.conf.d/80-intel-graphics-uxa-acceleration.conf file with this content: 

Section "Device"
  Identifier "Intel Graphics"
  Driver "intel"
  Option      "AccelMethod"  "uxa"
EndSection

This seems to have fixed that issue. Now I just need to figure out why the headphone's socket doesn't produce any sound, I can only get mono Bluetooth audio and the Bluetooth randomly turns off while I'm listening to audio.