I believe my firm successfully filed one against a field inspector before... he had spent all his time making stupid demands that went well above and beyond the code, holding up our project and killing our client's budget. Once his boss heard what he had been up to, she did the rest of the inspections on the job personally. So I guess our experience with it was good, but I'd still think hard before doing it because I doubt it always turns out like that.

louisville now has a system called metrocall which you can contact about just about anything. sounds like an empty service without accountability UNTIL you hear that every call or email is logged with an 'action' date. all files that don't get some kind of action within a month or so go to the mayor's office to be resolved. it actually seems to work. you might see if your area has a similar service.
here it's 3-1-1.

also, your permit reviewer has a boss - a director of the dept, even. they are responsible to you, a citizen.

most email addresses in city agencies are standardized now, so it shouldn't be hard to find out what the director's email address is.