I start this by saying that I know there are a number of different forms of feedback that general/artistic directors like and don't like.
I will also emphasize that good follow up doesn't guarantee a job, or make up for a bad audition.
However.....thoughtfulness is always noted, and I interpret it as a harbinger of good collegiality, punctuality, and preparedness.
So..how do you demonstrate thoughtfulness after an audition?
A note thanking your auditioner(s) for hearing you makes a positive impression.
While you certainly can do this by e-mail, I am of the opinion that a hand written note sent the old fashioned way will help cement a positive impression (assuming you have made that with your audition)
Why mail over e-mail?
It shows more thought and creativity - an e-mail can be whipped off quickly, and certainly is not a negative, but it can also be perceived as intrusive and pushy (I don't interpret it that way, but I know some people do).
A hand written note shows decorum, thought, creativity (your actual handwriting!!!), and professionalism.
I would be interested in hearing any one's experience with feedback......