Best thing to do? Don't drop your phone. I had a Galaxy SIII and every time it had a slight shake, the display would freeze and go all fuzzy. The issue was a loose display cable that wobbled a lot. You may want to check your phone for any damaged/loose cables since it's been dropped too many times.
Google Nexus 5 Black 16GB - Android L Preview
Samsung Galaxy SIII LTE i9305 16GB - Official CM11 Nightlies - AGNi Kernel.
HTC One X 32GB - CM11 nightlies - Faux kernel - Dead (bad build quality took it's toll.)
HTC Desire HD - Sold.