Working as a paparazzi is not illegal in and of itself but what the paparazzi is actually doing and engaging is violates privacy laws and it really should be stopped.
If someone else were to follow people around and snap several photos of that person and the person or people were not celebrities or famous for anything those people would call the police on them for stalking them.
Those people would likely be arrested and get into trouble for stalking but for some reason taking stalking photos of celebrities is not illegal.
But paparazzi have to follow strict laws and they can indeed get their self into trouble if they violate more of the laws than they can legally do.
I personally think there should be a law in place that puts paparazzi people out of jobs because it really is not right and is basically just legalized stalking.
Celebrities have a right to privacy as well and shouldn't be hounded and harassed just because they are famous.