Taking photographs and video of things that are plainly visible in public spaces is a constitutional right—and that includes police and other government officials carrying out their duties.
However, there is a widespread, continuing pattern of law enforcement officers ordering people to stop taking photographs or video in public places and harassing, detaining, and arresting those who fail to comply.
The right of citizens to record the police is a critical check and balance. It creates an independent record of what took place in a particular incident, free from accusations of bias, lying, or faulty memory. It is no accident that some of the most high-profile cases of police misconduct have involved video and audio records.