During the final fight scene between Jim and General Grimm, Grimm's hair changes back and forth from perfectly combed to wildly messed up back to perfectly combed several times. Grimm's character during parts of the fight is obviously a stunt double. Check his face.
When Jim fires the bullet at the blade of the axe, the bullet splits in two, and the two pieces pass on either side of Artie's head. The two pieces make two perfectly round holes in the wall, which would be impossible (or at least highly improbable). At best, one could expect two irregularly shaped holes as the two halves of the bullet tumbled after being split.
In the introductions sequence, West uses an elevator to ride to the fourth floor. When the doors open, there is no gap in the floor between the hallway and the elevator floor - it is one continuous floor. There should be a gap between the two floors to allow the elevator to move independently of the building.
In the closing scene, Musk asks Cloris for rouge. Makeup was not considered respectable at this point in American history, being more associated with prostitutes until around the 1920s.
During the fight scene in the pit, after Jim West knocks out the first two combatants and while he's fighting the third, the "knocked out" man nearest the fight keeps flinching when the fight gets close to him. Obviously not good at pretending to be knocked out.
When West shoots at Artie (as the Colonel), his instructions were to shoot from five paces away - but he takes six steps before turning to take his firing position.