Another problem with MTM is the fact that all the dogs, bears, and chickens and whatevers were in the manhattan melodies show and they magically know what to do in 2 seconds flat. As for the 2 weeks thing it was just a way for the movie, as you said, to have a ticking clock. These minor problems shouldn't stop you from loving MTM.
That's an old convention of musicals/productions that somehow have a musical number in it. It's never explained, it lacks realistic subtext, and generally makes no sense. Especially when the plotline calls for someone putting on a show. They do rarely show rehearsals after all... but they
really abuse that one when they think up a song
on the spot and the musicians
instinctively know what to play. You really can't blame the Muppets for an old, unexplained, convention like that.
The example that sticks out in my mind
hard is that episode of Ducktales where the Beagle Boys become a rock group because they were caught on stage trying to steal the battle of the bands cash prize. All the sudden, they have a perfectly performed song to which they
don't play instruments to (again, off screen, instinctive musicians).