In music lessons I want my students to strive to play a piece of music in the way that the composer intended it to be played. This is out of respect to the composer. Dynamics (loudness and softness) and phrasing (like how we talk in sentences and with expression) are used by the composer to show how they wanted the song to be performed.
As their teacher, I consider the piece played to perfection when all those musical markings are being observed. HOWEVER, I don't judge the perfection of a piece by how many mistakes the student made but by the overall interpretation and performance of the music. When the student follows the directions given by the composer it gives the music "heart" - a term that I use often when working with the student in the lesson. Music has to have feeling, not just correct execution of the notes.