Retired bishop of Clogher Joseph Duffy consistently missed opportunities to prevent clergy from sexually abusing children, according to the Catholic Church's watchdog.
The National Board for Safeguarding Children has published audits of several dioceses.
It states that in one particular case in Clogher, there was an unacceptable delay in taking action against a priest and removing him from all ministry following receipt of a credible allegation.
Another priest suspected of multiple abuse was transferred to another parish and eventually was sent overseas for therapeutic help.
He was later extradited to the Republic from the United States but died before he could be brought before the courts.
But the audit also states that under the leadership of the present bishop, Dr Liam MacDaid, the issue of safeguarding children is effectively prioritised in the diocese which covers Co Monaghan and parts of Donegal, Louth, Cavan and Tyrone.
Bishop MacDaid succeeded Dr Duffy in 2010.
Bishop Duffy was Bishop of Clogher for 31 years from 1979 and was spokesman for the Catholic hierarchy for much of that time.
In a statement Dr Duffy welcomed the review, which covered the period from 1975 to the present.
He said he accepted the criticism in the review and "regret that, in the past, the standard of managing some cases fell short of what is expected today".
Dr Duffy said the review is an important assessment of, and contribution to, maintaining a positive culture of safeguarding in the diocese.
He added that he is satisfied that the review acknowledges the effective child safeguarding structures and practice that operate in the diocese and which "I along with clergy and laity, spent many years developing in each of the parishes throughout Clogher".
Bishop says steps taken to deal with abuse
Bishop of Galway Martin Drennan has said the report into his diocese refers to three priests against whom allegations have been made, who are still in ministry.
No priests are named in the report.
Speaking on Galway Bay FM, Bishop Drennan said the concerns expressed were not of a sufficient nature to warrant their removal from ministry.
He said the HSE and gardaí had advised the diocese that what had been done, in terms of monitoring, was sufficient.
The bishop said today's report gave an objective view of the steps that had been taken to deal with the problem of abuse.
He said it showed the Church knew where it was going, had clear policies in place and that people could "trust each other in working together in a way we couldn't for the last 20 years".
The bishop said it had taken so long for this to happen because of the learning curve involved in understanding the problem of abuse.
He said very little was known about child abuse until the late 1980s and early 1990s and that understanding perpetrators and the effects of abuse took time.
He also pointed to the work that had been done to work out policies to respond to the problem as effectively as possible.
The report encourages better records be kept for meetings, decision making, planning and other discussions.
Bishop Drennan said it was his view that such a move would be "one factor that would make for better procedures".
The bishop said he was satisfied that the report showed all cases had been dealt with promptly and fairly.
He said it was a great consolation to him that outsiders who looked at things objectively had come to the conclusion that cases had been handled properly.
The bishop said he dealt with one of the cases mentioned in the report between 1975 and 2010.
He said the Church had "lived with a lot of bad publicity" over the last 20 years, which had tested the trust of people.
Bishop Drennan said the main message from the report was that it was safe for children to participate in Church-related activities.
Elphin meets 47 out of 48 criteria
The NBSCCCI's review of practice in the Diocese of Elphin has concluded that of the 48 criteria set out, the diocese has fully met 47.
It partially met one of them, relating to the gathering of feedback on policy and procedures from parents and children.
The review examined complaints or concerns received relating to 16 priests between January 1975 and November 2012.
It found that the incidence of abuse allegations within the diocese was not unusually high, but that they contain a significant number of allegations "which upon investigation were shown to be unfounded".
During the period examined, the review notes that 19 allegations were reported to the gardaí but no priests of the diocese were convicted of having committed an offence against a child or young person.
The work undertaken by the diocese on policies and procedures was very impressive, according to the review.
It noted that in general, allegations were reported promptly to the statutory authorities.
It found that in cases of delay, these arose through a belief that the allegation had already been reported or through a misunderstanding that another Church authority had already done so.
Up to 21 allegations against priests in the Irish Province of the Society of African Missions
A review of child sex abuse safeguarding practices in the Irish Province of the Society of African Missions has revealed that allegations of abuse were made against 21 priests from the province between 1975 and the end of last year.
Ten of those priests were still alive at the time when the review was conducted last December.
Two have been laicised, and an application has been made for the laicisation of a third.
The review states that just one of the 21 priests against whom an allegation was made was convicted of a criminal offence.
The review states that three priests against whom concerns were raised remain in some form of ministry in mission countries.
Following an examination of their cases, the NBSCCCI was satisfied that there were no child safeguarding issues to be addressed.
The Irish Province of the SMA has 193 members, of whom approximately 140 are still working while the remaining members are retired.
The Irish Province is engaged in missionary work in seven African countries.
It also runs two parishes in Cork city and a large retreat and conference centre at Dromantine near Newry in Co Down.
The review is largely positive, showing that the Irish Province has met most of the standards set down for the management of abuse allegations made against members and the structures in place for dealing with them.
The review team paid tribute to the commitment of Fr Fachtna O'Driscoll, who is leader of the Irish Province.
In a statement, Fr O'Driscoll said guaranteeing the safety of children is an on-going priority for the Society of African Missions.
He said he found the process of the review a constructive one which brought greater clarity to the society's work in this area.
A spokesperson for the Diocese of Waterford and Lismore said the audit acknowledged the positive work being done there.
He said there are good systems and practices in place and Bishop William Lee was strongly commended for his personal commitment and leadership in keeping children safe.
He said that of the allegations made against 15 priests, none led to criminal convictions.
The spokesperson said three of the priests are back in ministry and the allegations against one of them was acknowledged by the complainant to be false.
He added that concerns relating to the other two were thoroughly investigated and the priests were deemed to be fit to continue in ministry.
Meanwhile, chief executive of the National Board for Safeguarding Children Ian Elliot said he hopes 35 audits will have been published by the end of the year, which will include all 26 dioceses.
Mr Eliot also confirmed that he will be leaving the organisation later this year when his contract expires.
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