The problems with this film are...

Actually, you have it backwards-long takes are really MUCH more difficult and time consuming to stage because everything has to be perfect from the dialouge to camera movement, etc. One little glitch and you have to start over.
Chaplin, for example, used long takes all the time and he was one of the most meticulous of filmmakers-sometimes taking days and even weeks to get a particular sequence right.
It's much lazier to just film a scene from various angles and let the editors worry about putting it all together.
What's wrong with this film has nothing to do with the director's "laziness" and everything to do with his narcisim. Bogdanovich was riding a wave of success at the time and he simply believed that he could do no wrong (and he had no one to reign him in from his worst impulses). The fact that he would have even considered himself for the lead role pretty much tells us all we need to know about where his head was at back in 1974-75.

Agree with you completely though about the lack of story and dull characters.

With the exception of Kahn the singers just aren't very good.

They tried to sing live during the filming instead of dubbing it later which musicals with profession singers never even do.

Very little choreography. In many musical numbers the actors just stand or worse sit around.

It wants to be a screwball comedy, but none of the jokes are funny, and the pace is too slow for it.

One of the stars is almost unintelligible.

No chemistry between the romantic pairings.

Dull, lifeless, soulless, lacking energy. You really have to see this movie to appreciate how awful it is because no description will ever do it justice. Nothing is right with it, and everything is wrong with it.

And amazingly, a relatively forgettable collection of songs considering they selected a handful of Cole Porter songs. Of course all the above didn't help the songs any.