It is not illegal in the US. Airlines may have policies against it but that doesn't make it illegal and they sporadically enforce. Ultimately they may restrict your ability to fly with them. But you aren't getting a charge because you videoed on a plane.
Copyright???? what copyright would you be violating? You filmed the monitor of the safety video for monetary gain?
Privacy? You are in public there is no presumption of Privacy when you are in public even on a business' private property (Note: above policy may apply.
Audio however is more restricted in some states and you may require permission of those being recorded.