The plot has Fr. Michael running for the vacant council seat, but Church law prohibits a Priest from seeking or holding elected office as it is in direct conflict with his service to the church.
It has been pointed out that Fr. Michael would not be permitted by Church Canon Law to hold political office and at the time this episode aired, that is true, however, it is interesting to note that this was due to Pope John Paul II issuing an update to Canon Law in 1983 (10 years earlier) which eliminated a "loop-hole" from the 1917 version which permitted it if permission was granted by both their own Bishop and the Bishop of the territory where the election would be held. Since no dates are given in the episode, it could be argued that the episode was set prior to the change in Canon Law.