When McKeag and Clay Basket are readying for the Kiowa approach, McKeag cocks his rifle twice.
In the "Yellow Apron" segment (which timeline-wise would be around 1820), in attempting to break up the fight between McKeag, Pasquinel, and drunken soldiers, Major Sibley fires a revolver (possibly a Colt's Model 1849 pocket pistol), which was not introduced until the 1830s.
At the end of this episode, "The Yellow Apron", Pasquinel has clearly aged, his hair is white. And his two sons with Clay Basket are now all grown up. But Clay Basket herself hasn't aged a bit, she still seems to be about twenty years old. In fact her sons appear to be older than she is.