Murdoch indicates that one of the priests came from "St. Francis parish in Kitchener". The date of this episode would be ca. 1905. The city did not receive the name Kitchener until September 1, 1916. Prior to this, Kitchener was named Berlin. The name was changed during WWI. Also, St. Francis parish did not exist until after WWII as stated on the parish's web site.
When Detective Murdoch first addresses the bishop in the church, he addresses him as "Bishop." Per Catholic etiquette at this time-frame, the bishop should have been addressed as "Your Excellency," at least on first addressing him. The bishop could then ask to be addressed more informally, if he wished. When Murdoch and the bishop again speak in the cemetery near the close of the episode, Murdoch addresses the bishop as "father," which was/is not a proper form of address for a bishop.
When Father Jennings is in the pulpit close to the end of the episode, giving an explanation of events to the congregation, he is wearing his stole over his left shoulder across his chest (appropriate for a deacon) rather than over both shoulders as would be appropriate for a priest.