On-duty police can be filmed in public and private places

Washington Post/Volokh conspiracy - First Amendment right to videotape police extends even to probationers, and to one’s own home as well as public places

This is a report from a case recently held where a police officer went to search a suspect's home, and during that time, the suspect recorded the search. The officer had a right to search the home since the suspect was on "searchable probation" [presumably, allowing her to be searched at any time for whatever reason]. During the search, the suspect informed the officer that she had her laptop on and was recording the search of her residence. The police officer told her recording wasn't allowed, and took away the laptop and deleted the video. The suspect filed suit that her first amendment rights were violated. The court agreed. While most cases have involved the right to film the police during prosecution of their duties in a public place (as long as such filming doesn't interfere), this court extended the right into the private residence of the individual as well, with the proviso that the individual has a right to be in that residence.