Previously Sully said when his wife Abagail died he went East and joined the Army. Now he says he would have died if Cloud Dancing hadn't found him and taken him in. Writers must not be talking to each other.
Colleen was shown wearing new pierced earrings after Dr Mike pierced them, but at the 30:57 min mark her ears are naked and unpierced.
Matthew tells Colleen that she's looking at her silver hand mirror so hard it will break, but previously it was already broken by the visiting orphans.
Sully keeps using the word AHO as a hello greeting. Aho is a Lakota Sioux word, not Cheyenne, that means 'it is good' and is sometimes said following statements or prayers.
It was wrong of Hazen to announce Sully's monthly salary publicly in the saloon.
As Sully is being sworn in you can part of an American flag. The stars are in the configuration of the flag that was in use from July 4, 1865 - July 3, 1867. According to the time line of the show this episode is in 1870.
Matthew has 171 beef cattle. The cost of feeding them must be overwhelming. Matthew should have offered to sell or give some cattle to the Indians.