A man who returned from overseas three days after the lockdown says controls were incredibly weak after he arrived at Auckland Airport.
The man, who did not want to be named, told RNZ he was twice blocked from domestic flights and instead was shuttled by bus between the airport and a downtown hotel four times.
It comes as Prime Minister Jacinda Ardern is promising stricter border controls after an epidemiologist warned that without urgent tightening of them, lockdown should not be lifted.
Ardern said there was no evidence of broad flouting of self-isolation but wanted the system improved.
"We are looking again to leave no room for error at the border, and so I warn New Zealanders that you can expect that at our borders we will be expecting more of you," she said yesterday.
The man told RNZ he and his partner were stymied from catching a domestic flight, and as a consequence they were shuttled by bus between the airport and a downtown hotel four times, to and fro.
He said, when they got back to the hotel a second time, Ministry of Health representatives told them they could go out and have a coffee and use the supermarket.
"We were basically told, look until things are sorted out, feel free to hop into the hotel, you can check out again later if you do another isolation plan or if indeed there is a flight for you," he said.
"But in the meantime, you can go across the road and get a cup of coffee, or you can actually go to the supermarket."
The couple thought this contravened all the self-isolation rules for travellers.
"When we expressed surprise about being able to go around to the corner to get something from the supermarket, we were told that it was against our human rights to be contained, and that we were actually able to do this, to go around the corner.
"I mean, it was just incredible."
They decided to self-isolate properly, so got a car from the airport and drove to a house provided for them.
Five days later, last Thursday, they got a smartphone message via the police app, seeking to pinpoint their location.
It achieved that, and looked reasonably official, the man said, but this and another contact, from the Health Ministry's Healthline, were too slow.
"It was a bit too long. And I think it's early in the process, but I would have thought as part of a self-management plan, we would have given instant authority for access location devices to be turned on.
"I would have expected that kind of thing. And I think that's a perfectly reasonable thing to do.
"One of the biggest problems is a disease coming in from international. So I think a lot of effort's got to be targeted at that chink in the armour.
"You know, you're only as good as your weakest link... From our experience it was incredibly weak when we arrived."