I don't know which system you have specifically, but here are some basic tests. With the engine idling, attach a vacuum pump to the EGR and apply vacuum. The engine should stumble or die.

This is the test I used to check my EGR. Sure enough the engine stumbled and started to die when applying vacuum with the pump. For some reason the top of the EGR was capped off at the end. It looked like an adapter to make the hose fit better but upon further inspection it was just a cap. Also installed a new Knock Sensor, unhooked the neg terminal for a bit while I cleaned up the shop. When I hooked it back up I took it for a drive and no CEL (was getting a code 71 and 52). Before it was coming on about a minute or two into the drive; about when i hit 20-30 mph.
I was also getting the vibration at idle, when stopped at a light or whatever and that is just about gone also.

So hopefully that problem is solved. The last tank before the fix averaged about 15 mpg. Now that these two things are fixed should my gas mileage improve? If not what to look at next?