Skegg said although it may take several hours or more than a day to collate that information, it needed to be made public.
"It's unacceptable that that information is not provided," he said.
"There must be records of each and every one of those people who were released into the community on compassionate grounds."
"We ought to know exactly how many of those people there were and also whether they were let out on the second day, the third day, the eighth day - or whatever."
He said that information would help to predict the "undetected problem" that we may have.
Asked if he was worried about reports that birthday parties and other celebrations were held inside hotels among passengers isolating, he said he was.
"They actually destroy the purpose of quarantine because someone may have been infectious and infected someone perhaps on day 10 of quarantine and they won't even develop symptoms and become infectious until after they've gone into the community."
Skegg said it was therefore imperative that even passengers arriving on different days and at different times were kept separated, even at the same isolation facility.
Skegg scoffed when asked about revelations from some new arrivals that they were told the swab test was not mandatory, but voluntary.
"I'm amazed to hear that people are being given a brochure at the airport to say that the testing is voluntary. People should be quite clear that if they're coming here, part of the deal is that you go into quarantine or isolation for 14 days and you are tested.
"I can't understand how that ambiguity has arisen."
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Despite those issues, Skegg also praised the country's efforts to eliminate Covid-19; but acknowledged some of that might also come down to luck.
"We've achieved a fantastic result here in New Zealand. We're the envy of the world. We've really dodged a bullet in terms of the health consequences, but also our economy is recovering faster than other countries.
"So we've really done well. But we've put it at risk with this kind of shenanigans."
Skegg ended the interview by pointing out one thing New Zealanders may need to work on moving away from - complacency.
"I've always thought that is our biggest risk and, certainly, this bears that out."
Bloomfield admitted he did not know how many people had left quarantine hotels without being tested before Tuesday - but insisted he does not need to quit following revelations of various bungles.
"I haven't quit. I am not planning to quit. I have worked hard to keep New Zealanders safe," Bloomfield told Hosking.
"It's clear ... we didn't meet expectations and I'm sorry about that."
The mainstay of protecting the border was 14 days of isolation, he said.
"We have had managed isolation for several months ... we added the testing at level 1. It didn't get implemented as well as it could have."
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Bloomfield's comments came as two women - who travelled here from the UK - were allowed out of isolation at an Auckland hotel early and without being tested. They made a road-trip to Wellington and took Covid tests there that turned out positive.
Despite initially saying they had not contacted anyone on their road-trip, it was revealed yesterday that they came into contact with at least two friends who helped them after they became lost on the Auckland motorway.
An Auckland gym member is believed to be one of the friends who "kissed and hugged" the women after helping them.
Bloomfield said this morning it was a "fleeting interaction" and both those friends had been tested and were now in isolation.
"We wouldn't even usually consider a close contact," he told RNZ.
"They were not hugs and kisses. There was a very fleeting arm put around the women to provide comfort.
"This was so fleeting that actually, the women themselves who were very distressed did not recall that happening."
