I'm currently leveling my umpteenth alt, a druid healer, almost entirely through LFD. Even at level 45, I've seen great PUGs and horrible PUGs and everything in between. A bad group can be moulded into a good one by a few calming words in chat.
"Everyone focus on the tank's target please, you can't expect him to keep aggro on everything at this level."
"DPS please watch your aggro. You're bleeding me dry!"
"Let's keep it together guys, only one boss to go, and then we can all get blue gear we don't need from our satchels."
You'd be amazed how the presence of one vocal, sympathetic, and laid-back party member can coerce the others into better behaviour.
Of course it doesn't always work. There are utter idiots out there who are numb to the gameplay experiences of every other player around them. But sometimes spending a little effort to hold the group together can pay great dividend.
I also think there is something about the healer role. PUGs which might laugh in derision at a tank asking for patience will for some reason pay attention to a healer saying the same thing. I can't quite explain it, as both roles are equally essential.
As I don't have the rep to post comments yet, I will say that no matter how tired you are of running the same HC, it's not the newly-geared tank's fault, so don't take it out on him. If you really have no time for helping a newb get his gear, then stick to guild runs.