Nothing like that. If you don't sell drugs or waving your AK-47 out in the open, if you don't attack other people and not running around naked, there's really nothing to be afraid of (from the police). Sometimes loud voices (or shouting, etc) can attract some attention, but nothing serious would come out of it (especially, if you're obviously - a foreigner).
Oh, don't try to participate in some civil protest actions - you can end up in a police station.

No matter what happens - just don't panic when police approaches you. They're mostly civil and polite. They will ask you for some documents and walk away. You might have heard some horror stories about militia but if you haven't done anything - there's little to worry about. Even if they detain you - you'll be released in several hours (in the worst case, provided you're a law abiding tourist).
If they try to extort a bribe - haggle (arguing or refusing will cost you several more hours of wasted time - they'll release you anyway, so if you have spare time just ask to inform the ambassador or your country ))). Tell them you don't have much, you're a poor person and you've been saving for this trip during the last decade. You can even shed a tear or two... (no, really). Avoid aggravating them. Be calm and polite (even if they don't).