One of the main mistakes that I often see from new Tai Chi students is what we call in our school the "wandering eye". It's easy to spot if you're watching the student perform but one of the harder habits to train out of someone.
Wandering eye is simply where the student is performing a form but their eyes are darting everywhere. As cliché as it sounds, the eyes are truly the doorway to the soul and a wandering eye means that the mind is not focused and thus not centered and absorbing the good energies being generated.
In external Martial Arts, it's much easier to find focus. The practioner has a target to strike and thus a place to send their energies. The mind is focused on these external targets and thus the eyes tend to focus on observing the movements of the opponent and projecting the attack.
In internal Martial Arts, such as Tai Chi, the practioner must focus internally. There isn't necessary the same projection of external threat. Furthermore, the object of the internal arts is to draw the energy in, not send it out. So, projecting outward to a target will actually send the energy away from the body and disrupt what is trying to be accomplished through Tai Chi.
What happens is that the student's thoughts wander. Did I remember this or that? Should he/she be doing that over there? Wonder what's for dinner? … etc. And when the mind wanders, so does the soul and thus the eyes.
There are a few ways to train out of the wandering eye. First off, you must become aware this is happening. Awareness is the key to correcting any situation but it's often not enough. One can't simply "hold down" your eyes and make them focus inwardly.
I generally instruct people to start practicing more meditation. The object of meditation is to focus the mind inwardly and prepare the body. The more meditation one does, the easier it becomes to find that point of focus and enter it.
Another method to use is to visualize where the energy is moving in the body. Every movement in Tai Chi sends the energy to different parts of the body. If one can visualize it being drawn in from the feet and then circulating through the body with each movement, to focus naturally moves inward and to the energy.
If you don't improve right away, don’t fret. It takes time and practice, as in anything in Martial Arts, to grow and perfect. The more you practice with awareness, the better you will become. And soon, you'll not suffer from the "wandering eye."