So, compiz is the culprit, no surprise there. I was thinking this is a problem deeper in the system, but thankfully, that's not the case. 
Resetting Compiz to the default settings may help. You can do this by clicking Reset Compiz in MATE Tweak (providing Compiz is actively running) - this will erase any customizations if you made any.
If that doesn't work, you can downgrade the package via Synaptic, like so:
Compiz highlighted → Package → Force Version...
Choose the older version, if available.
After locking the version, you may need to re-install what will now be the older version.
Coincidentally, compiz is upgradable for me via Synaptic, but I will wait until it appears in the Software Updater - in case it breaks my system too!