Commissioner Costigan was involved in the security for the visit of then President John F. Kennedy to Ireland in 1963. Three death threats had been received and Commissioner Costigan warned his subordinates to not disregard the possibility of any such threat, no matter how implausible the source. He regarded Kennedy'sstate visit as the most significant event in the country's history since independence.
The Murphy Report criticised Commissioner Costigan for his handling of allegations of child abuse by Fr. Edmondus. Scotland Yard had contacted him concerning images that the priest had sent to be developed in the UK. Commissioner Costigan asked Archbishop John Charles McQuaid to handle it because a priest was involved and he claimed "Gardaí could prove nothing".