The ACLU sought to prevent and or document the abuse of citizens by police. In some cases the ACLU actually provided people with cheap video cameras to record their encounters with police. The ACLU asked the U.S. District court to invalidate the law [preventing such recording]. That matter has now been fully litigated and it is the law of the land throughout America. Citizens can record their encounters with police without fear of arrest.Huebl details the full back story, here.
If you plan on filming the police, carry a note in your wallet that reads: U.S. Supreme Court decision in the case of the American Civil Liberties Union versus Anita Alvarez, so that you can show the reference to the police, if the police try to hassle you.
If you are planning on regularly filming the police, print out a page of key excerpts from the decision and carry it with you.