/var/log/syslog constantly logging errors, growing at 1 MB/s

Solution 1:

You have the latest hardware - Skylake came out Q3-2015, Z170 board as well. The 4.2.0 kernel came out at the same time, so development for it was before board and CPU were widely available. Mint 17.3 is based on Ubuntu Trusty, which is even older.

Try with a Live CD of Ubuntu Xenial to see if your hardware is better supported by kernel 4.4.0. If you want to have the latest hardware, you better run the latest Linux on it for best support.

Even the current beta of 16.04 probably is a better fit for your system, with less issues.

EDIT: To have a quick fix for the issue at hand, do sudo echo "disable" > /sys/firmware/acpi/interrupts/gpe6F. This should temporarily disable the GPE and get rid of the messages. You probably need a BIOS update to fix the issue.