Libertarians typically refer to the Non-Aggression Principle (NAP), where your right to swing your fist stops at my face.
It would be hard to argue that filming the officer violates the NAP, particularly since the officer is allowed to film another individual citizen, creating a parity of individual rights.
I see what you're trying to say about coming at the problem from different perspectives, but the individual liberty arguments are almost always going to be the simpler ones to reason about when starting from first principles. The common good arguments become subjective and ambiguous very quickly. Worse, the people making the collective arguments are almost always the ones with the power. Guess which arguments will win out most of the time.
As a left-libertarian, the NAP is the kind of sophistry that makes me not consider right libertarian truly libertarian, as taken to the extreme it can be used to actively deprive others of even the right to life, reducing liberty more than it increases it. (Most commonly is it used to protect property rights)
E.g. if I monopolise all sources of food, strict adherence to the NAP prevents you from using violence to prevent everyone else from starving to death.
The left-libertarian view would be that the right of life is far more essential to liberty than property rights - if you are dead there is no way you can be free -, and so if many are at the threat of starvation over your property rights, liberty is maximised by taking your property from you, even at the cost of your life if necessary, as your act of monopolising an essential resources is morally equivalent to violence against everyone deprived.
This is a common good argument and individual liberty argument at the same time.
At the same time, though, I believe that any adjudication based on individual rights would need to consider the totality. E.g. police officers from the outset are given substantial rights that infringe on our personal liberty ostensibly out of the belief that doing so will protect us against grater infringements of our personal liberty.
Being allowed to film them, then, while it may on a low level infringe on an officers individual rights, can also be seen as protecting the individual rights of others by providing oversight on the special rights police has been granted.
The officers have an easy out: They can surrender their special rights to infringe on others liberty, and we'll surrender any special rights to infringe on theirs.
For my part I think that whether you look at this from a common good or individual rights perspective, as long as you look at the totality, you can arrive at pretty much the same outcome.
Where you get a different outcome is in how you weight different rights up against each other, and how you determine the totality of infringement caused by different actions.
E.g. you could (and to be clear, I strongly disagree with what I'm about to describe) argue that the officers have a right to privacy or to avoid harassment or similar that outweigh the public concern over monitoring their use of their expanded powers if you see their potential to infringe on others rights as leading to less infringements on liberty than the infringements of officers rights by allowing them to be filmed.