I mean a military base far away from any war zone, such as a tank that has been abruptly called out due to a riot or other disturbance. It wouldn't be heavily battle-worn obviously, but how would it look?

If it's been in a base far from the frontline it'll be quite clean (unless it's been taking part in a training excercise, where you'd expect some dirt and scratches in high-traffic areas) and well looked after, so no rust at all. Hope this helps!

First World AFV's will be well-maintained and painted. Third World AFV's may show faded paint and visible rust. If the vehicle is operating on paved roads, it will acquire a fine layer of road dust, mostly on the lower hull and suspension. Recessed areas of metal track may exhibit a patina of rust. Any metal that contacts the pavement or contacts other metal moving parts will be bright steel (i.e. drive sprocket teeth).

On dirt roads, it will get dirtier, faster.

I thought of several such scenarios, one of them being a revival of my Tiananmen Square idea. The problem would not be getting the vehicle so much as Chinese rioters in civilian clothes. Haven't been able to find anything so far.

Maybe see if you can find any civilian figures and find some replacement heads?

Like those released by Firestorm :

http://www.firestormmodels.com/store/home.php?cat=97&sort=orderby&sort_direction=0&page=1

H.P.