Legally, videotaping police officers is not against the law, and those acting under "color of law" instead of actually enforcing actual law are routinely smacked down by constitutional law when challenged. Their is no right to privacy unless there is "reasonable expectation" of such, and being in public is not such a place. I even got Homeland Security to go away with their tails between their legs while videotaping at federal courthouses when they attempted to impose "made up" laws. :D
But there are cases where gestapo agents will illegally detain people exercising their basic rights...the supreme court has ruled clearly on this type of bullshit already...but that doesn't stop thugs of the government trying to trick you into doing what they want or illegally harassing you sadly.