Hopefully there will come a day when most citizens are armed with video cameras and are anxious to record the police. This will drastically reduce the likelihood of police abusing their power.
Police expect citizens to comply with their demands, and contempt of cop is the most common cause for abuse. When police ask you to put your camera away or to show them your papers, what can you do? In most states, if there is no expectation of privacy (out in public) it is not illegal to video tape. Some advocate that you should not say anything to police, EVER.
Some might ask the police to show you the law which says you have to stop recording or show them your id. If they say they cannot provide the document which states this, then you could say: "Well I can show you the law which says you cannot harass me". And you could show them the 4th Amendment which states: "The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
Arm yourself by checking your local laws.
Are politicians thinly masked maniacs?
Getting arrested for jaywalking
Oscar Grant getting shot in the back
Charged with felony for recording police aggression?