I ran the UV benchmark app. I did a few runs with stressful settings and had absolutely no graphical errors, glitches, boxes or otherwise.
I seem to primarily get the problem in my task bar area and in Final Fantasy 14. The task bar can appear whenever, even right after I load up the machine after getting home from work or what not. I've also gotten the weird boxes to appear when using Firefox fairly frequently.
The part that confuses me is the random boxes when I haven't even used any programs or games yet. A single game, maybe driver issues, whatever so on and so forth.