Hank was sentenced to 6 months in jail, so he should not have been out to do anything. Correction: The six month jail sentence was changed to a fine of $100. Matthew convinced the judge in Denver.
Teresa Morales keeps referring to the boarding house but there is no such boarding house in town. It became Dr Mike's clinic years ago. Correction: Multiple people have mentioned a boarding house. It is possible another one was opened off-screen.
Jake was given modern wedding vows. Back in 1872, vows would have contained the word OBEY.
Michaela and Sully rode out to retrieve Cloud Dancing from from the Army on 4 horses, then rode into town with him on 5.