After his first performance, Cheyenne is changing in his dressing room. As he turns to get a shirt his bare back is clearly visible, and no scar from an arrow wound can be seen. Later, when his "wife" spills cleaning fluid on him deliberately to try and verify his true identity, a substantial scar is shown on his back.
During Cheyenne's first meeting with supporters of Baylor's 27th Calvary, he holds up the flag of the 27th in front of the group. A closeup shows Cheyenne unfurling the flag and holding it with the front of the flag facing the group, showing the number 27. But a moment later a shot from the rear of the room shows Cheyenne holding the flag backwards, with an inverted number 27 clearly visible.
The Ford Theatre poster announcing the play misspells "repertoire" as "reportoire".
The song, "Some Sunday Morning", was first introduced in 1945 in the movie, "San Antonio", sung by Alexis Smith.
Cheyenne sings on stage a song called "The Deadwood Stage (Whip-Crack-Away)" with music written by Sammy Fain & lyrics by Paul Francis Webster. It was written for the 1953 Warner Brothers Doris Day-Howard Keel musical Calamity Jane. Both Cheyenne the series and Calamity Jane were both Warner Brothers productions, so it makes sense they would borrow from one source to use in another.