There are lots of healthy foods out there. Even if a food is healthy there can be problems if a diet isn't diverse. Scurvy is one of the more common problems that can occur due to a lack of vitamin C. One of the more surprising problems I came across is eating too much corn which if not prepared well can cause delusions and even death.
As long as a wide variety of foods is eaten then there usually isn't a problem unless allergic reactions are involved. At that point there's no telling what can come up.