Remember that police officers are still normal citizens, too, with the attendant rights and protections thereto. If you followed me personally around with a camera 24/7, that would be harassment. If you just followed me around 24/7 without a camera, that would be harassment. By "harassment" I don't mean necessarily that exact legal term but I'm sure there's some legal recourse if such a thing happened.

We don't necessarily need lots of "special" rights to film police, we just need them not to have special rights not to be filmed.