Suppose someone is a dual citizen, with two passports: NZ and somewhere else.
Must this person enter NZ on their NZ passport?
(This is the case for US passport holders - when entering to the US - to my understanding)
It is not required for a New Zealand citizen to enter using a New Zealand passport.  However, if the person intends to stay longer than what would normally be allowed by a tourist of the nationality of their passport, they would have to prove their NZ citizenship in some way.
For example, a dual Mexican/NZ citizen who only holds a valid Mexican passport, would be allowed to enter New Zealand for up to 3 months under visitor visa rules.