This applies for the EGR system on M112 & M113 engines (and possibly others if they use the same EGR valve & solenoid). This fix could possibly work; there are no guarantees. But trying this first is surely a lot easier than replacing the valve - and it can possibly save you a fair amount of time, effort, and money if it works. I hope this write-up may be helpful for other people in the future...

First and foremost, do a couple of quick diagnostic tests. These do not require a vacuum pump nor disassembly of anything other than taking the connector off of the EGR vacuum solenoid valve. (It would be ideal if you had a vacuum pump to test everything, but it's not an absolute necessity when using these methods.)

1.) With the engine off, run test leads to the EGR solenoid valve terminals and listen for it to 'click' when voltage is applied. If you hear a (faint) click, it indicates the solenoid isn't dead, and you can proceed to step #2. If the solenoid IS dead, you are SOL and will need a new valve.

2-a.) If the engine idles smoothly:
With the engine idling, apply voltage at the solenoid valve. With voltage applied, the engine should start misfiring and running very rough. Remove the voltage and it should return to a smooth idle. Do this several times to see if the response is consistent. If the response is consistent, then the vacuum solenoid is working, vacuum is being applied to the EGR valve's diaphragm, the diaphragm rod is opening & closing the internal pintle valve, the EGR tube leading to the intake manifold is flowing, plus the purge valve is working. That's relatively good news, as it means those components are all functioning correctly... so your problem lays elsewhere.
Diagnostic result: If the engine does NOT respond to this test by idling roughly, then attempt the cleaning procedure outlined below and cross your fingers.

2-b.) If the engine idles very poorly:
This could possibly indicate that the EGR valve may be in the open position during idle, which is improper. So...
While idling, disconnect the electrical connector from the EGR valve's vacuum solenoid. If the engine smooths out, the vacuum solenoid is staying open when it should not be. But it IS closing when the connector is removed, indicating that voltage is present when it should not be. That would indicate a fault of some sort which is causing the ECU to supply voltage to the vacuum solenoid when it should not be doing so. This would be relatively good news, as (again) the EGR system's physical components are functioning... but you'll need to dig elsewhere to cure the improper signaling problem.

If the engine does not smooth out with the vacuum solenoid connector removed, leave it unplugged and feel around to find the vacuum hose leading to the EGR's vacuum diaphragm canister. Carefully twist & pull vacuum hose off of the canister. If the idle smooths out, reconnect it to see if the idle deteriorates again. Do it several times to check if the response is consistent. If doing this results in a smooth idle whenever the vacuum hose is disconnected, then the vacuum solenoid valve may be stuck open or leaking internally - so attempt the cleaning procedure outlined below and cross your fingers.

3.) Testing the vacuum purge valve and the EGR valve functionality:
Note that this test will work ONLY IF all the other physical EGR components are functioning properly.

Scenario "A": When the engine is idling smoothly:
Apply voltage to the vacuum solenoid valve. If the engine begins to run roughly, but does NOT smooth out again just by removing the voltage AND does smooth out when you remove both the voltage and the vacuum hose leading to the diaphragm, the vacuum purge valve is not functioning properly. The good news is the EGR valve itself is functioning properly, the EGR line is flowing, and the vacuum solenoid is working. BUT... the vacuum solenoid could still be working only intermittently, thus causing an intermittent problem. I'd suggest that you pull the purge valve off to clean it, and also clean the vacuum solenoid valve as described below.

Scenario "B": When the engine is idling poorly:
Remove the vacuum hose leading to the vacuum diaphragm. If the idle does not smooth out AND the rough running condition is absolutely known to be attributable to the EGR system, this means the EGR valve itself is stuck open and will require replacement. Or you could take it off and try to clean it, but success isn't guaranteed with that approach.

If the idle DOES smooth out when the vacuum hose is removed, reconnect it and apply voltage to the solenoid valve. IF the engine begins idling poorly again with voltage applied, but it does NOT smooth out again when voltage is removed, the purge valve is not functioning properly - so attempt the cleaning procedure outlined below.

(Note: The vacuum purge valve is the black plastic disc shaped device freely hanging off of a vacuum line attached to the underside of the vacuum solenoid valve.)

Cleaning procedure:

First a word of warning: In this procedure you will be working with highly flammable materials and producing a spark when connecting and disconnecting an electrical device. Not generally a good combination. This necessitates taking precautions and paying attention to what you're doing. If you lose your eyebrows or turn your car into a flambe' of melting metal, plastic, and rubber... don't say I didn't forewarn you. BE CAREFUL!

To energize & de-energize the vacuum solenoid valve, polarity doesn't matter. Use either a pigtail connector or otherwise clip your leads into place securely. I used alligator clips, but that is not ideal as they can easily be knocked loose and create a spark right where you don't want it. You'll want to make or break the circuit as far away from the flammable vapors as possible.

Access to the EGR valve may require removal of the intake air tube on some models, such as on the W210's. Once you have good access to the EGR valve area, do the following:

Apply voltage to the vacuum solenoid to open it. Disconnect the vacuum hose at the diaphragm canister. Spray some brake cleaner or electrical contact cleaner into the hose. (I strongly suggest to NOT use carburetor cleaner, as it is much more aggressive to rubber and plastics!)

Start the engine, and while it is running (and thereby creating suction on the disconnected vacuum line when the solenoid is energized) spray short blasts of the cleaner into the vacuum hose. While spraying the cleaner, repeatedly connect and disconnect the solenoid valve, which will help the cleaner work itself into the valve and flush out any contamination. Do that a few times, then turn off the engine, fill the hose with cleaner and let it sit for a few minutes. Repeat the process a couple of times.

After cleaning the solenoid, run the engine for a few minutes with the solenoid energized to allow it to dry out internally. Then while turning the solenoid on & off again, spray a couple of very short blasts of silicone spray into the hose to internally lubricate the solenoid valve. NOTE: Silicone is known to poison oxygen sensors and catalysts, so use the smallest amount of silicone spray as possible!

For the purge valve, spray the brake or electrical contact cleaner into it to flush it out, and follow that with a little silicone spray to lube any internal components. Ideally you would be able to connect it to a vacuum source to suck out any contamination too.

That's it. Reconnect everything and cross your fingers. It may or may not solve the problem. But if it does work (as it did for me) then great - you've saved yourself the additional & unnecessary effort of removing the EGR valve, and saved yourself a nice chunk of money too. GOOD LUCK!