He was consecrated on July 25, 1901, by Cardinal Sebastiano Martinelli at Holy Name Cathedral in Chicago.

Some of these discontented priests engaged in character defamation against Muldoon - one of them was ultimatelyexcommunicated by Feehan for these actions.

While there was some support for naming Muldoon as the new archbishop, that initiative was abandoned in the face of his previous opposition in Chicago.

[1] Muldoon later told a friend that he was worried his enemies in the archdiocese might assault him due to his appointment.

[1] In December 1916, the Vatican indicated its interest in appointing Muldoon as bishop of the Diocese of Monterey-Los Angeles in California.

[3] With the 1917 entry of the United States into World War I, Muldoon became active in ministering to soldiers and recruits at Camp Grant, the US Army facility in Rockford.

[3] In 1919, after the end of the war, Muldoon persuaded Cardinal James Gibbons to propose to the Vatican the creation of National Catholic Welfare Council (NCWC), a peacetime organization that was comparable to the National Catholic War Council.

With Vatican approval, the NCWC was created in 1919 with Muldoon as episcopal chair of its Social Action Department.

In his vision for the NCWC, he supported a paper on social reconstruction written by Father John Ryan.

After the American hierarchy sent a delegation headed by Shrembs to Rome, the Vatican agreed to restore the approbation providing, among other things, that the organization be renamed the National Catholic Welfare Conference.