For anyone with a deep fascination or interest in 3D animation, and in particular, 3D character animation, the goal is often to gradually improve the standard of your character animation to the point where you are not afraid to show it to even the most critical audience.
One aspect of character animation, which can be difficult to get a good grasp of, is eye movement. It is easy to underestimate just how vital it is to get the animation of the eyes right in your scenes, and in particular, in close-ups of your 3D character. There is nothing that screams "beginner" more loudly than slow, lazy, left-to-right and back again eye movements. Eyes simply don't move like that... unless you've been drugged, of course. And unless you inject some life and vitality into your characters, through their eyes, they will always look dead and lifeless on screen.
To see a really excellent example of the right way to treat this important and often overlooked area of character animation, take a look at the DreamWorks film "Shrek The Third". While the story and general animation are good enough to hold most people's attention, the eye movements of the characters in the close-up shots is absolutely fantastic! A superb example of the difference a little observation of life in action can make to an animation.
Time for a practical demonstration. Try this - hold your hand up in front of you and look at it. Notice that your eyes do not simply fix on a single point on your hand without moving. They dart from one place to another from your fingers to your palm, to your ring, back to your palm, up to your thumb. It is this continual movement of the eyes from one focus point to another that you must capture in your facial animation if you want your 3D character to look like they have something going on in their head. It is this continual movement that is a noticeable feature of the animation of Shrek. When he is talking to Fiona his eyes move in a shaky, imaginary triangle drawn between her eyes and her mouth. Notice the next time you are talking face-to-face with someone that these are the three points on their face that your eyes most often dart between.