[3] Law was widely denounced for his handling of the sexual abuse cases, and outside the church his public image was destroyed in the aftermath of the scandal.

Two years after Law resigned from his position in Boston, which Bishop William Skylstad called "an important step in the healing process",[4] Pope John Paul II appointed him Archpriest of the Basilica di Santa Maria Maggiore in Rome in 2004.

[16] He was made a member of the Vatican's Secretariat for Promoting Christian Unity and served from 1976 to 1981 as a consultor to its Commission for Religious Relations with the Jews.

[16] In 1981, Law was named the Vatican delegate to develop and oversee a program instituted by the Congregation for the Doctrine of the Faith in which U.S. Episcopal priests would be accepted into the Catholic priesthood.

Geoghan had previously been known to abuse children, and at least one auxiliary bishop in Boston warned Law that the priest was unfit to return to parish ministry.

[11] The bishops' report concluded that "the principles and basic rituals of Masonry embody a naturalistic religion, active participation in which is incompatible with Christian faith and practice".

[23] Reporter Kristen Lombardi, who was assigned to investigate by Susan Ryan-Vollmar, the editor of the Boston Phoenix weekly,[24] wrote "Cardinal sin", an article about the cases.

[5] Even though abuse by Geoghan had been reported repeatedly in the media since 1996, the new editor of the daily Boston Globe newspaper Martin Baron set the Spotlight investigatory team to work on the case in September 2001.

[25] In April 2002, following the Boston Globe's public exposure of the cover up by Cardinal Law (and his predecessor Cardinal Humberto Medeiros) of offending priests in the Boston Archdiocese, Law consulted with Pope John Paul II and other Vatican officials and said he was committed to staying on as archbishop and addressing the scandal: "It is my intent to address at length the record of the Archdiocese's handling of these cases by reviewing the past in as systematic and comprehensive way as possible, so that legitimate questions which have been raised might be answered.

[29] The Globe's exposé of the scandal was the subject of an Oscar-winning film, Spotlight released in the United States in November 2015, in which Law was portrayed by Len Cariou.

[24] In a statement, Cardinal Law said, "It is my fervent prayer that [my resignation] may help the Archdiocese of Boston to experience the healing, reconciliation and unity which are so desperately needed.

[24] When the state attorney general issued his report entitled Child Sexual Abuse in the Archdiocese of Boston (July 23, 2003), he severely criticized Law, mentioning that "the Archdiocese has shown an institutional reluctance to adequately address the problem and, in fact, made choices that allowed the abuse to continue," but did not allege that Law had tried to evade investigation.

[32] In May 2004, Pope John Paul II appointed Law to a post in Rome, as Archpriest of the Basilica di Santa Maria Maggiore, a largely ceremonial role.

[36] After his retirement in 2011, Law continued to live in Vatican City, and regularly attended the annual July 4 Independence Day parties held by the United States Embassy to the Holy See.

[38] He visited the United States for the last time in August 2015 for the funeral of Cardinal William Wakefield Baum in Washington, D.C.[39] In May 2012, the National Catholic Reporter and The Tablet, a British Catholic weekly, reported that Law was "the person in Rome most forcefully supporting" Baltimore Archbishop William E. Lori's petition to investigate and discipline the Leadership Conference of Women Religious, a large group of American nuns.

[5][39] His funeral rites, following the standard for a cardinal who dies in Rome, included Mass in St. Peter's Basilica on December 21 at which Pope Francis said the final prayers.

[43] Upon his death, his successor as Archbishop of Boston, Cardinal Seán O'Malley, OFMCap, said it was "unfortunate" that Law "had such a high-profile place in the life of the Church".

[44] The Guardian noted at the time that Law had become "a symbol of the Roman Catholic Church's systematic protection of paedophile priests" because of his refusal to stop sexual abuse in Boston.