The valve itself has two failure modes, stuck open or stuck closed. You'll need a vacuum pump to diagnose it. In it's normal operation, the valve is closed and exhaust gases are unable to flow from the ports in the cylinder heads, through the intake, through the EGR spacer, through the valve, and back into the intake, through the spacer. When the valve itself fails, either the diaphragm ruptures or the pintle on the valve becomes caked with carbon and sticks open.
Step one, engine off, apply vacuum to the valve and see if the valve holds vacuum. If it does, the diaphragm is good. Next, look in the openings in the side of the valve for movement when vacuum is applied. If it is, the diaphragm in the valve is good, and the valve is free to move. The next step, engine still off, reconnect the vacuum line to the EGR valve, and remove the cover on the passenger side wheel well to access the vacuum solenoids. The solenoid which controls the EGR valve will have three solenoids, the one you'll be concerned with has (or had) a green plastic line connected to it. Disconnect the vacuum line from the solenoid, connect a vacuum pump, and verify the line and valve hold vacuum.
The next step is done with the engine on, the EGR vacuum line disconnected and plugged (I generally use a golf tee). Connect the vacuum pump, start the warmed engine, and let it idle. As you apply vacuum and open the valve at idle, the engine should stumble, this tells you the ports in the head and intake are clear and the valve is operating.
The other point of failure is with the vacuum solenoid. You can test this with a vacuum pump and a 9 volt battery (or jumper off the car battery). You will disconnect the solenoid, apply vacuum to the lower port (I think, the hose that isn't green). It should hold vacuum, and when power is applied it should release.
To determine if the valve is original, look at the engineering number on the valve. If it starts with E5TE, it is original, if it starts with E5PE, it is a replacement.
I see a lot of posts on here of people blocking off the EGR valve, and I've never understood why. At rest, the pintle is closed and the valve doesn't flow inert gas. You could disconnect and plug the vacuum line and the valve or at the solenoid, or unplug the solenoid and get the same net result. The whole idea of the EGR valve is to introduce inert gas during cruising to lower combustion temperatures. If working properly, it's your friend.
A common failure point relating to vacuum operation on the 2.8 is the vacuum reservoir (coffee can). It's located on the passenger inner fender and holes can rust into it. After the engine has been running and shut down, disconnect the vacuum lines feeding it, you should hear air rush in. It's a worthwhile exercise to get a vacuum pump and disconnect all vacuum lines (one at a time) at the control solenoids, and test the operation of the attached devices (and check for leaks). The design is really a feat of electromechanical engineering and works well when all pieces are intact and properly functioning.
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