What are some signs of mental illness in a child?

Erratic behavior. Mental illness is an extremely broad term. Any obvious and persistent abnormal behavior might be questioned.
Withdrawal. In addition to dr. Lonsdale's answer about erratic behavior, I would also add that things such as a long-standing withdrawal from the family and peers could be a sign that consultation with a mental health professional might be indicated. Also, extreme fatigue, trouble concentrating, sleep problems, and chronic negativity could also be a few more markers of inner turmoil in a child.