Privacy and the government is a critical theme throughout Dredd. The increased surveillance of citizens in Mega-City One is a product by the massive crime rate, caused by the unemployment and over population. Since the central characters Judge Dredd and Judge Anderson are government workers, the audience is given a direct view as to the powers of the government has, and therefore the lack of privacy of citizens.
We see that in the beginning of the movie that using drones the government can scan citizens and pull up their information in a central data-bank. We also see the security system in the Peach Trees mega-block which relies heavily on CCTV cameras, and seems to cover all hallways and public spaces. The Peach Trees security system however does not cover every room of personal home, showing the government in Dredd doesn't have the resources to cover its entire presence.
Another interesting privacy concern is that of Judge Anderson who is a psychic government employee. At multiple points in the story she uses these abilities in order to gain information from the minds of both suspects and random civilians that would otherwise be impossible to attain. Breaching into the mind of someone who is resisting intrusion is a type of surveillance which is incomparable to any technology which we currently have access to. This raises pressing questions as to whether there are any limitations at all to the government of Mega-City One, since you don't even have the right to security of your own mind.