If your job as a cop is hindered by being videotaped while in public areas, then your job is by definition not in the public's interest, and you should not be allowed (and especially paid) to conduct it.
I know the real world is different than most people think, but I also think most of the pressure to break the law probably comes from having to enforce laws that shouldn't be on the books anyway, like drug laws.
For instance, certain organized crime and/or labor union groups will often threaten reprisals against individual cops who enforce the law against them. If you're a cop whose job it is to escort people across a particularly unruly picket line then I can see how you could reasonably object to being 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.
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.
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.