The FMA said the issues went back as far as 2001 but its claim reflected the introduction of the Financial Markets Conduct Act 2013, which came into force from April 2014.
The regulator claims ANZ contravened section 22 of the Act by making false and misleading representations about the cover of the policies.
"The regulator is seeking declarations of contravention of the Financial Markets Conduct Act, pecuniary penalties and costs."
ANZ itself reported the issues in June 2019 and has already compensated customers to the tune of $440,000.
But the FMA claims the bank knew about the duplicate policy issue around September 2017 and the ineligible customer issue around May 2018, but did not declare it to either the FMA or the RBNZ during their joint conduct and culture review of New Zealand's retail banks from May to June 2018.
That was despite the review specifically requesting ANZ disclose "any work underway to remediate any identified issues where conduct by your firm has resulted in detrimental outcomes for customers".
ANZ has acknowledged it took too long to report the issues but has pointed to the small number of customers affected - 307 - and the fact it has apologised and compensated affected customers.
The regulatory legal suit comes on top of a class action it is facing from investors in the failed ponzi scheme Ross Asset Management (RAM).
Last month, the High Court at Wellington declined ANZ Bank's attempt to get a suit from more than 500 investors in RAM thrown out early.
Instead, the judge ruled the $80 million class action would go to trial.
The investor case alleges David Ross' former bank, ANZ, knew certain payments misapplied RAM client funds and the bank dishonestly assisted RAM's breaches of trust, benefited from charging fees and interest through RAM's misused overdraft, and breached a duty of care in negligence.
Ross Asset Management was the country's largest ponzi scheme when it collapsed in late 2012.
More than 800 investors believed more than $450 million was being managed on their behalf but actual losses were closer to $100m. About $10m has been recovered.
ANZ has previously said it would strongly defend the claim and that it too was misled by Ross.
Last month, the Reserve Bank also noted in its financial stability report that it "continues to work with ANZ to address and gain assurance in the areas of non-compliance identified in both [section 95] reports".
The banking regulator requested two independent reports from ANZ in June last year on the bank's governance, risk management, internal controls and risk capital models.
The first report, released in December last year, made a raft of recommendations resulting in the RBNZ requiring ANZ to engage an external party to confirm before the end of 2021 that it had implemented all of those changes.
A second report, which assessed the bank's capital adequacy requirements, found there had not been sufficient rigour in ANZ's processes which led to the failure of the issues not being identified.
All of it points to the level of change needed at the bank.