The sign outside of the doctor's house says his name is Emmet Sloane. However, the end credits say that the name is Sloan.
When Artemus, disguised as General Robert E. Lee, claims custody of the gold and supplies from Captain Lyman Butler, he is wearing the wrong rank insignia. Lee wore the rank insignia of a Confederate Colonel. Which was highest rank he obtained as a US Army officer. Butler, Artemus, and Jim would have known this.
When West uses his pistol to shoot the anchors into the wall (in the mine), the sound is muffled, as if a silencer were used - but there is no indication of a silencer (which wasn't developed until after 1900 anyway).
The second time James West fires his arrowhead gun, the "rock" wall can be seen bending slightly as the arrowhead penetrates it.
At the very beginning, Jim and Artemus ride up to the edge of town. However, "Artemus" is actually a stunt double.
The caves are very well lit throughout, even though there's no electricity at the time of the episode's time-frame, nor are there torches lit.
When Jim and the Captain are looking at the map, as the Captain moves to the left side of the map, the camera casts a very large rectangular shadow on the map.