No. It's never reasonable to prevent a record being made of the actions of a police officer.
In the case of undercover officers, it is reasonable in some cases to to hide the fact they are police officers.
I believe there are cases in which police may seek and should probably be granted the ability to obscure their identities, while still acting as uniformed officers, for specific operations. The Mexican police who took down a major drug lord recently all wore balaclavas and helmets in public, for this reason. This needs to be justified on a case by case basis or you will get abuse (like the cop who attacked Ian Tomlinson).
But in every case, their actions should be legal and legitimate. They should having nothing to hide.
While I agree that it should be allowed to tape any interactions you have with an officer, it's a bit of a gray area if you follow one around taping everything they do.
First: they are off duty sometimes (they get breaks too)
Second: They are dealing with other people, and that interaction deserves a level of privacy as well. If I follow a officer up to a car stop, and start recording, that seems intrusive.
So, the question is where the limit of permissible is. Do off duty police officers have normal citizen rights to prevent themselves from being taped? Do on break officers have that? How about on duty officers talking with another person? Can I record that audio? Video?
In my mind it should be more permissible than taking video of normal people, but a blanket "lets tape everything" doesn't work either. Where exactly the correct middle ground lies isn't clear to me.
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.
In the case of undercover officers, it is reasonable in some cases to to hide the fact they are police officers.
I believe there are cases in which police may seek and should probably be granted the ability to obscure their identities, while still acting as uniformed officers, for specific operations. The Mexican police who took down a major drug lord recently all wore balaclavas and helmets in public, for this reason. This needs to be justified on a case by case basis or you will get abuse (like the cop who attacked Ian Tomlinson).
But in every case, their actions should be legal and legitimate. They should having nothing to hide.