See the attached US DOJ letter to Boston Police Counsel. 
It cites numerous court opinions that the people have rights:
- To record and photograph police in performance of their duties, so long as it does not interfere with that performance;
- To direct vocal complaints at the police during the performance of the duties for the manner of performance, so long as the complainant does not use “fighting words.”
- Terms like “son-of-a-bitch,” “asshole,” and “someday you’re gonna get yours” do NOT constitute “fighting words” and DO fall within the meaning of protected speech under the First Amendment, according to court rulings.
I specifically recommend:
- FOR recording the police and chiding them for inappropriate behavior, both personally and in writing to Internal Affairs (every police department has an IA group that aims to penalize police for corrupt or illegal behavior).
- FOR keeping a safe distance from police during such recording.
- FOR remaining mobile and physically fit so one making such recordings can escape from any incidental personal danger.
- AGAINST using hate speech against policemen
- AGAINST making one’s presence, equipment, or recording obvious to police in the performance of their duties. Police remember the legal backlash against the LA police for beating Rodney King – a citizen recorded the incident and released it to the press.
- FOR releasing to the media and Internal Affairs any such recording one might make.
- FOR ALWAYS OPERATING WITH A CREDIBLE WITNESS NEARBY during any engagement with government personnel, particularly DANGEROUS personnel – one’s witness should become a witness only, apart from any fray and from one’s observation and recording. A credible witness can mean the difference between one’s liberty and one’s incarceration because juries nearly always believe law enforcers over defendants. Naturally, the witness should record one recording the incident so as to have a record of any police interference with the recording.
As to recording, it makes sense to prepare oneself with eyeglasses that have a built in HD recording camera ($25). Police might not readily recognize the eyeglasses as a recording device, whereas they definitely recognize cell phones and handheld cameras as potential danger to them, then snatch and destroy them or delete the recorded images. 
Thanks to Earl F for the heads-up.