I have liked that manga, it has insipired me to keep going with the music.
I haven't been neither in a conservatoire or in another music school yet, but I think that the manga is accurate in the part of learning and how to achieve goals in the music world, how there is people who have some advantages and disadvantages and how they have to deal with them.
However, as you said, there are many things which are over-exaggerated and romanticized.
There was a part where Chiaki was forced to sign a contract to work as conductor, it was exaggerated because in real life, one would see this as a piece of luck because it is difficult to get work.
And about Nodame's ability, I admit that she is put as a tremendous prodigy, that she has almost perfect auditive skills and she had a good memory in difficult pieces (although that skill was based in her strong self-determination), skills that couldn't appear from the nothing, skills that should have been cultivated since long ago (like doing a split). However, according to the story, she also has faults in her playing.
I know it is almost impossible that someone has her incredible ability, but I learned that she also has to struggle with her faults in playing like everyone else in this world.
Have you read also Piano no Mori?, it would be the same issue: the main character has a progidious mind in music (only that he has all the musical skills almost at 100%), but also he has to deal with issues which you may be familiarized like stage panic.
The idea of Chiaki about how to play the piano is very accurate to what schools want and expect, while Nodame's idea is more romantic, to play the piano the way you like, but at the same time can guide you to love the music as an amateur (a person who doesn't play in a professional way).
Embarassing to ask, but...