What is wrong with a 16 year old who hasn't had a period in a year?

Probably Nothing: Teenagers are immature hormonal and this leads to sporadic ovulation. Ovulation is key to maintain and regular menstrual cycle. Without ovulation, months can go by without a cycle. This is extremely common in teenagers and typically regulates over a period of time.

Doctor Evaluation : A year without a period isn't normal if she was already menstruating. When we see girls in the office for this, a variety of things have to be ruled out, though the most common reason is polycystic ovary syndrome. Many other things can cause this as well: large weight fluctuations, poor nutrition, chronic illness, thyroid dysfunction, other hormonal abnormalities, etc.