Irish police commissioner Nóirín O'Sullivan has said revelations over penalty points and breath test discrepancies are "unacceptable".
The Irish Labour party leader said almost one million drink-driving tests recorded by police in the Republic of Ireland did not actually take place.
Brendan Howlin called for the head of the force to be replaced.
Senior Gardaí (police) conceded it was likely some of the 937,000 non-existent tests were simply made up by officers.
In addition, they have admitted a separate error that caused almost 15,000 wrongful traffic convictions.
Gardaí have apologised to those affected, but fixing that mistake alone could cost Irish taxpayers millions of euros.
Ms O'Sullivan said on Saturday that the police service was on a journey of radical reform and "it is inevitable that we will identify more examples of bad practice".
Earlier, Taoiseach (prime minister) Enda Kenny said the revelations over discrepancies were "not acceptable".
Minister for Justice, Frances Fitzgerald, said the scale of the error was "appalling and staggering".
The details of both problems were released by senior officers on Thursday, when a lot of media attention was being devoted to the Westminster attack and the funeral of Sinn Féin's Martin McGuinness.
The force revealed that about 14,700 people had been prosecuted without a fixed-charge notice first being issued - which was required to bring them before the courts.
Officers now have to appeal all those convictions; have the court-imposed penalties removed; and the state has to cover all costs.
Ms O'Sullivan said she has written to the Policing Authority seeking further review by the garda inspectorate of the discrepancies between real and claimed breath tests.
She said it is a problem that goes back more than a decade and that new processes for gathering and collating statistics have been in place since April 2016.
Ms O'Sullivan said that the Policing Authority and Garda management are of the same mind that the discrepancies identified in the systems are a "matter of individual and collective ethical behaviour and not one of occasional systems failure".
She was already facing questions over her leadership because of allegations of a smear campaign against a whistleblower, Sgt Maurice McCabe.
Sgt McCabe was one of two officers who raised concerns years ago about the alleged deletion of penalty points from the driving licences of well-connected offenders.
The leader of the Labour Party said the latest controversies were "beyond belief" and had seriously undermined trust in An Garda Síochána.
In its statement on Thursday, An Garda Síochána said a review of its breath tests data was carried out after concerns were raised in 2015.
Data recorded on the Garda computer system - known as Pulse - was compared against data recorded by the Medical Bureau of Road Safety and a "significant deficit" was identified.
'Questions of integrity'
Officers said the Pulse system recorded 1,995,369 breath tests while the Medical Bureau of Road Safety Data recorded only 1,058,157 tests over the same period.
"There is no one single reason that may account for the discrepancy," the Garda statement said.
It is not the first time in recent months that Garda figures have been dismissed as lacking credibility and trust.
Last September, the Central Statistics Office said that up to one in six crimes were not being recorded by Gardaí on their Pulse computer system, which meant - either intentionally or unintentionally - inflating their crime detection rate.
The Policing Authority, an independent body that oversees the performance of An Garda Síochána said this latest controversy over figures "is not just an academic statistical matter, it is an ethical one".
It also said the controversy "raises serious questions of integrity" for the force.
Child abuse smear
In 2012, Sgt Maurice McCabe was banned from using the Pulse computer system after he accessed records of penalty point cases.
Last month, it emerged under parliamentary privilege that senior Garda officers are accused of spreading a false smear that Sgt McCabe had been liked to a case of child sex abuse.
Commissioner O'Sullivan strongly denies allegations that she was involved in any smear against him.
The accusation against her force is now the subject of a public inquiry, headed by the Supreme Court judge, Peter Charleton.