Since The Byrds chose to play "Not Fade Away" instead of any of their
other songs, and evidently saved "Mr. Tambourine Man" for last, it is
reasonable to assume the June 23, 1965 date of that Shindig! TV show is accurate.
According to Byrds biographer Rogan, the "Mr. Tambourine Man" b/w "I
Knew I'd Want You" 45rpm single was released on Monday, April 12, 1965;
the "All I Really Want To Do" b/w "Feel A Whole Lot Better"
45rpm single was released on Monday, June 14, 1965; while the Mr. Tambourine
Man LP album was released on Monday, June 21, 1965. So The Byrds were just
getting started with radio airplay, and the Mr. Tambourine Man LP album had only
been out for two days at the time of their Wednesday, June 23, 1965 Shindig!
TV appearance. Consequently, "Mr. Tambourine Man" was undoubtedly
their only recognized pièce de résistance at that time, which was probably
why it was saved for last on that early Shindig! TV appearance.