New Zealand Law
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Unfortunately this is not something which can be covered by The Privacy Commissioner. They do not have jurisdiction over the news media, but the place to complain about this is as follows:-
For complaints about newspaper reporting, the agency to contact is the New Zealand Press Council (www.presscouncil.org.nz) by calling (04)(###) ###-####
For complaints about television or radio reporting, the agency to contact is the Broadcasting Standards Authority (www.bsa.govt.nz) by calling 0800 366 996.
In addition, where the news footage is not relevant to the story and is unnecessarily intrusive, this can be considered a breach of privacy under the tort of privacy. That would require a court case unfortunately. I suggest that you start by contacting the people who made the documentary and seeking removal of the personal information, and if they refuse, then try the Broadcasting Standards Authority.