At the beginning of the film, after Logan deposits his gold, he is shown crossing the street in the rain. In the long shot he gets one foot on the sidewalk, but in the next closer shot he is still a few feet from the sidewalk and then steps onto it again.
Oregon 1856? AirPlane engine can be heard (appx 1:29:32 of 1:32:14), at the burnt down cabin scene. When Logan Stuart approaches Johnny Steele, and Steele draws his weapon.
The Indian maiden swimming in the stream is quite obviously wearing a 1946 style 2-piece swimsuit.
The women are wearing modern undergarments (bras).
When people are shot by an arrow, there is obvious padding underneath the costume.