Strawman Has a Point: George makes legitimate points about how he and his fellow travelers were kidnapped and brought to Shangri-La, and that it's better to try and make The Outside World a better place rather than hide away and wait for it to be destroyed.
In the films, the Wise Man describes the civility of their society, and how terribly rude it would be to express interest in a woman that another man wanted... unless you wanted her desperately, in which case he would of course yield her to you. The woman's opinion is apparently irrelevant. In the book the conversation goes like this: It would be rude to express interest in a woman involved with another. What if you want her so much you don't care about courtesy? In that case it would be polite for the others concerned - including the woman - to humor you.
As discussed at length in Musical Hell's review of the 1973 version, Shangri-La — a society that isolates and indoctrinates outsiders into a very specific belief system, discourages dissention, has next to no contact with The Outside World, and in fact is waiting for the outside world to destroy itself whereupon the utopian society will be the focal point of a new and better civilization — is effectively a Cult, and thus extremely creepy by modern standards.
Narm: A lot of the musical numbers end up as this, but especially the infamous "fertility dance", performed by dozens of muscular men in orange loincloths. After audiences broke out in laughter at the initial screenings, the dance was cut out of all future prints of the film. Long believed lost, it was restored in the 2011 DVD release.
Narm Charm: Enough people view the film as this to give it a cult following.
Older Than They Think: This wasn't the first time the story was tried as a musical. Shangri-La, which was done with the full blessing of James Hilton (he even worked a little on the book before his death), opened on Broadway in 1956 but closed after 21 performances.
Unfortunate Implications: In her review of this movie, Diva of Musical Hell points out the very strong Mighty Whitey themes of this movie, since the High Lama is white and wants a white man to succeed him. She goes on to say that this might not be so bad if not for the fact that the Asian characters are one-dimensional and often stereotypical. Putting John Gielgud in yellowface and calling him "Chang" certainly doesn't help, and neither does Shangri-La lacking a decent irrigation system until the white engineer comes up with one. This wasn't even Values Dissonance; even at the time, Pauline Kael declared that it was rather suspicious that the film's idea of a utopia was a society where white people rule over Asians and black people don't exist.
Liv Ullmann, the face of moody European art cinema at the time, as the female lead in a dopey The Sound of Music copycat? Bette Midler once quipped about this, "I never miss a Liv Ullmann musical." Believe it or not, the public would get another chance to miss a Liv Ullmann musical in 1979, when she starred in a disastrous Broadway version of I Remember Mama, which was even written by The Sound of Music's Richard Rodgers (his final musical, as it turned out).
Peter Finch and Michael York play siblings, despite Finch looking old enough to be his father (at the time of filming, York was almost twenty years Finch's junior).
In general, casting the majority of the leads with people who could neither sing nor dance.