Curiously, she doesn't mention two things that I've always thought as essential to good spins:
1) Spotting - Let the head be the last thing to go and the first thing back. Sometimes spotting alone can increase the number of turns one can complete in a short period of time. Secondly, much less force is required in torque through use of the arms, shoulders and hips when spotting is employed. Also, spotting makes the turn appear much faster to the observer.
2) Stopping - the ability to stop a turn at a predictable time shows good balance and makes the turn appear much faster to the observer. Settling into the hip helps in this regard. Try to think of settling about a half turn ahead of the actual stopping point. More drastically and for added effect, one can extend the arm to the side. For example, if you are spinning to the left, bring your right arm from the center of the body to the outside for a nice effect.
3) I know I said two, but I thought of one more point. On solo turns, try bringing both arms tightly into the body after the second spin, and chances are you'll be able to add one more turn than you were able to do previously.
4) Stance - this makes 4...I'm on a roll. On the step preceding the turn, make sure the feet remain close together. Nothing ruins a good spin like a wide stance.
Edie is a wonderful dancer and I am in no way trying to claim some level of higher knowledge. I just thought these things were worthy of addition and/or discussion.