One of the easiest mistakes to make when drawing or painting a portrait is to make both sides of the face symmetrical. No one is symmetrical, and the few people who are almost symmetrical have a very eery feeling about them (some people think it looks beutiful but it makes me feel uneasy). Brad Pitt and Angelina Jolie are two good examples of people with almost symmetrical faces.
So I'm looking at reprints of artist's work at the library the other day and I come across a book on Hans Holbein. He's famous for painting portraits, many of which were for royalty at the time, but its his drawings that I find particularly exceptional — more specifically, the eyes. What I notices is he always pushes the differences between the eyes to the point that its slightly exaggerated. The eyes are one of the central defining factor as to whether a portrait works or not, so by pushing the subtleties in their differences you end up with a very powerful representation of that person's unique expression.
Check out how the far eye is drawn much larger than the closer eye. This plays with the perspective of the face, pushing the far side of her face forwards and as a result her whole face looks wider and flatter:
The difference in the way the eyelids fall over each eye: