I second The King of Drama!
And there's also
You're Beautiful for an insight into music production.
Oh and also
Mary Stayed Out All Night, has a little bit of both drama and music production on the background, it really isn't the main focus of the plot though.
Being a huge fan of the manga and anime, one of my faves is Taiwanese though:
Skip Beat! it shows the backstage of acting in dramas better than probably any other one.