Apparently you can try cleaning it with an eraser, but I'd just replace it myself. Also apparently,
you can get a new pot without spring for the whole new airflow meter but it is difficult to calibrate it. That said I know a dutch guy who did it with no problem at all. I replaced the whole AFM - about £300.
As for the EHA current you need to put one probe into one socket and the other probe into the other socket. To test current through the multimeter. But I guess you are doing this already. You will notice the idle change when you do this as control back to the EHA or idle speed regulator resumes.. I find it utterly useless BTW to measure these sorts of things with a digital meter, thats why I have two - the analog one you can see trends with and they are cheap as chips so maybe get yourself one of these?
So anyway it sounds like the pot could be part of your problem, be sure to check duty cycle when you have it all back together as per Steve's article.