Halvorsen's "scar" on the left side of his face moves around. When he is hiding out, it runs down his face between his nose and cheek. When he wrestles with West, it's gone. Then when he's in jail, it crosses over his nose.
Benito Juarez was 4'6" tall, but the actor playing him looks to be at least 6' tall.
When describing to James an altercation with Colonel Gonzalez Artemus continually refers to her as a "hot tomato". That term did not originate until the 1920s.
Early in the third act, when Lupita is threatening the disguised Artemus Gordon, the knife she is using is obviously rubber. As Artie turns to face her, the blade can be seen to drastically bend against his chest and then snap straight with a jiggle.
(at approximately 0:04:45 - early in the first act, just after the opening credits) West drops down from the top of a wall, and, as a result, the rear seam of his pants splits wide open, revealing his white underwear. West turns his exposed backside away from the camera and goes on with the scene just as if nothing had happened.