[8] In 2000, he conducted an inquiry into Donnchadh O'Buachalla, a judge of the District Court, over allegations of bias in overseeing the grant of a licence to operate the Jack White's Inn pub to Catherine Nevin, who was a friend of O'Buachalla's.
[10] In the Supreme Court's decision in Maguire v. Ardagh, arising out of an Oireachtas inquiry into the death of John Carthy, he was one of two judges to dissent.
Murphy and the Chief Justice Ronan Keane held that the Oireachtas did have such power.
[15] In 2002, he was appointed to chair a three-person non-statutory commission to review historic allegations of sexual abuse in the Roman Catholic Diocese of Ferns.
[18] The Ferns Report was published in 2005 and was strongly critical of the handling of allegations by the Catholic Church.