First, many dancers frown in concentration as they turn, especially if they're struggling. But that stiffens the muscles in your neck and jaw, which makes spotting nearly impossible—and, in turn (hah! see what I did there?), clean pirouettes difficult. Smiling will relax your face, allowing you to spot more naturally.
But there's another advantage to putting on a happy face. A recent study showed that tension in the jaw was often connected to tension in the hips and pelvis. So relaxing your jaw will also loosen up your hip joints, creating more space for rotation and making for a cleaner, better-balanced passé.