The fact that at least in your experience, something in the code (mozilla firefox?) appears to
help trigger the graphics issue, may lead one to attempting to suggest this matter to Mozilla
so they can look into the build codes in their Firefox browser. Maybe it has some parts that
do not fair well when in use among other system or application codes; or with the firmware.
There is a feature in Firefox browser to report an issue; however the real proof would be in
the lines of system information relating to whatever is happening in your system. And that is
where this problem may find some resolution, if the right people actually had access to the
unit and the in-situ problem generated by the configuration of software & hardware inside.
{I've not upgraded my Late 2012 Mini i7 quad server beyond as-shipped OS X 10.9(.5) and
when I bought this unit from Apple Store online (clearance/new) hoped that it would be an
older stock model with Mountain Lion, since it shipped with only 4GB RAM. However I have
not done much with the computer, & could have saved $1K by exercising pre-buyer remorse.
Have considered partitioning one of the two factory installed 1-TB HDDs so as to create a
space for later OS X installations, while leaving the original Mavericks installation intact; but
did not hear back on inquiry, if I could do that and get the application upgrades, (as offered
to new computer purchases) installed in the second HDD as well, and so I haven't. A year
ago on 23 December; so I'm considering Applecare plan. Unanswered questions there, and
lack of on-ground support in AK have left me wondering why I bought such a new item; as
I've much previous experience using & repairing older model Macs...}
Anyway, if Mozilla were able to make head or feet out of your situation, given the error message
or line of code from terminal or other internal complication due to the combination of their Firefox
and the later version of OS X in the hardware of your Mac Mini... that would be a rare incidence
of someone noticing a problem exists and seeking a cure for only one model series involved.
As I've said before...
Good luck & happy computing! 🙂