Reddit mentions of Peter and the Starcatcher: Acting Edition (Peter and the Starcatchers)

Don’t read directly off the page. Look down as often as you need, but look back up to deliver the lines.

Don’t let the page in your hands prevent you from incorporating physical action into your audition. If your character is dancing or exercising or cooking dinner, go ahead and play that out instead of using the script as an excuse to stand planted in one place.

Don’t forget to respond to what you hear and what actually happens, not what you read. Make sure that you are taking the cues for your own lines and emotions from your partners, just as you would with a memorized text. Their tone and energy should be incorporated into your audition, not suppressed and reimagined as whatever you first thought when you read it on your own. The cold read part of an audition is often a chance for the director to see how two partners work together in the roles, so make sure to play the partnership.

Finally, if you know the show you are auditioning for, or if the sides are available, then it’s doesn’t have to be a cold read at all. Familiarize yourself with it to the greatest degree possible. If you are “cold reading” Arthur Miller, you should not be reading those lines for the first time in your life. If you are “cold reading” Shakespeare, you should have a very good sense of the characters, relationships, and story at least. In this case (Peter and the Starcatcher) the script is readily available. Hie thee to a library and do as much prep as you can.