When Father Parker is at the freight line looking for work, Mr. Stokely offers him a job. Mr. Stokely tells him he owns the saloon. But the first episodes explain that Paul Garrett owned the saloon, then in "Matthew and Elizabeth" ownership passed to his brother who had been in prison; the manager of the saloon welcomes him and Garrett thanks him for managing it until he could get out of prison. Therefore Mr. Stokely only manages the saloon; he doesn't own it.
Right after the long scene when Father Parker talks to Rita about her future, as the bouncer throws a man out the front door he apparently hits the camera a little--it visibly shakes.
Closeups of the piano man (Max Segar) look like he isn't playing it; the finger movement and the sound doesn't quite match. But where it really shows is when Rita goes up to the piano to sing; his hand barely moves in the middle of the keyboard but higher notes are heard.
When Mr. Wade enters the saloon to shoot O'Bannion, Father Parker jumps in to stop him. Mr. Wade says "I don't know you." Father Parker then says, "I know you, you go to Catholic Mass on Sunday." This indicates he is a parishioner. How could Mr. Wade not recognize Father Parker? He's not in his monk habit, but his face and voice are the same.