This summer when I auditioned actors for a short film I had a PA take copious notes in the anteroom as the actors waited to be called. Their behavior while waiting was almost as important as their performance during the audition when it came time to cast. We knew we'd only have one looooooong shooting day and needed both a talented and patient cast. We also needed some minors and their parent/guardian behavior was also noted...did they try to interfere? Did they bring something to do to pass the time?
Sometimes what you look for might be spontaneous. At the same audition there was one young lady who read absolutely dreadfully...she couldn't pronounce certain simple words, she stumbled over simple phrases, etc. A nervous bundle of poo that completely botched her read. But she had a look and other indescribable qualities that were dynamite...a unique face and structure and...something...that was one in a million. I called her back in and just started talking to her, asking her whatever questions came to mind...where did you go to high school, what did you study in college, what is your favorite television show, what is your favorite thing to do on a Sunday afternoon, etc. I was trying to determine if she could be calmed down enough to speak clearly, and in that 10 minute simpleton conversation I had seen enough to know that she could...she could be coerced gently into delivering a simple line or two and wouldn't screw anything up. That night I rewrote the script and included two new lines for this actress specifically. She botched her audition but a part was invented just for her and she NAILED IT at the shoot.
And second to everything already noted...you're looking for the right person for the part, you're looking to how well they take direction and adjust their read based on notes you give them, you're looking at how well they use a partner, you're looking for strong choices (even if they're not the right choices). I love auditions...it's where you first get a chance to see your words (or the writer's words, if not you) come to life.