First, I would verify with those folks that told you someone expressed concern, that there were multiple people and not just one person who said something, or, even that they were trying to be passive aggressive in telling you that they don't like it. Have dealt with people in gov't, you know, probably better than anyone, how some people can be. Then I would explain to them the reasoning behind it and make sure that they are cool with it (after all, the City Manager is your boss, I assume). As long as the Manager says it can stay, I would ask them to get the name and number for anyone with a problem with it so that you can call them directly. Not to be confrontational, obviously, but, I think, that it would be good PR for them to hear directly from the Police Chief about their concern. And, again, as you know, there is probably only about 5% of any population that cares enough about the little things like that about any City/County gov't, so there would not be many calls for you to make; and after a while, I can't imagine that it would not just go away. And I really do think that that would be great PR.
I think that the tinting is important. Not only from a privacy issue (which is the only issue angle you have with people). But also, from a less official standpoint, there are things that Dispatchers should be able to do, WITHIN REASON, to relieve stress while cramped up in the Comm Center. Stress is, debatably, the number one issue facing overworked, underpaid, unequally recognized Dispatchers. And it is important for them to be allowed to get up and walk around and even laugh and joke around with co-workers while on duty (provided it doesn't interfere with their work) during the less busy times. And you don't want the public to see this, but it is very important for employee mental health and morale. If you have them in view of the public, there is, obviously, an expectation on them to promote professionalism, likely disallowing them to have any of these freedoms.
That last part is, obviously, my opinion. But, as a manager, I feel very strongly about creating a work environment for our Dispatchers that take as much stress off of them as possible.