This is an excellent movie; I really enjoyed it. The two major stars are Jimmy Stewart and John Wayne but Vera Miles (The Posse That Wouldn't Quit), Andy Devine (The Men That Corrupted Hadleyburg) and Jeanette Nolan (Pilot) also star.
It was really interesting to see them when they were younger; the movie is from 1962. Miles and Devine looked basically the same, although Devine was somewhat heavier. Both Miles and Nolan spoke with Swedish accents, which was a little weird.
A couple other things connect The Man Who Shot Liberty Valance to ASJ: In the beginning, during a stagecoach robbery, the leader of the gang says, "Stand and deliver!" I was surprised to hear it so I looked up the phrase and discovered that highwaymen said this when they robbed their victims and, according to Wikipedia, the phrase was in use since the 17th century.
And at the end of the movie, there's a reference to Junction City--it must have been a popular place since it's the second time I've heard it mentioned in a Western, and this movie was a Paramount picture! The plot, told as a flashback, revolves around something Stewart's character did. I'm not going to say anything more about what happens in the movie: Just go watch it!