Age of actors versus roles
In 1962 John Wayne was 55 and Jimmy Stewart was 54. For Jimmy and the Duke their ages are really 'showing' in this movie. And, for the period the movie takes place in both of the men are past average life expectancy. In other words, they both would have been considered to be very old, in the old west.
Though I have always appreciated The Man Who Shot Liberty Valance for story and production the ages of the male leads has always been a major negative to me. This isn't a radio play and the way the actors look is important.
Stewart, in particular, had many roles in the the 1950's where a younger actor would have been more appropriate. By 1962 somebody else should have landed the Stoddard part. He was just too old.