SSH on Mac to fresh install of Firefox on 64-bit CentOS 6.4 runs but generates errors: RANDR and GLib-GIO-WARNING
For the first warning on RANDR, try installing a newer version of xquartz

Searching there just now, it looks like randr was added. I can confirm that on my system which is running xquartz 2.7.4 on OS-X 10.7.5:

$ xrandr -v
xrandr program version       1.3.5
Server reports RandR version 1.3
$ sw_vers | grep 'ProductVersion:' | grep -o '[0-9]*\.[0-9]*\.[0-9]*'
10.7.5




For the last warning, does "update-mime-database" exist on the system in the user's $PATH?