When you mention the "heterogeneous nature" I assume that you are talking about how American schools can differ radically in quality and funding from district to district and state to state. This difference is a major factor in one of the biggest problems we face, which is the problem of a lack of good education for students from poorer areas of the country.
As the New York Times link below discusses, a major problem with American education is that students from poor areas don't get a good education. This comes quite directly from the heterogeneous nature of our system. In our system, students in rich suburbs attend schools with lots of equipment and good teachers while rural or inner city students attend schools that don't have the facilities and don't have the wealth to attract the best teachers. The same difference exists to some degree between rich and poor states. In this way, the heterogeneous nature of the school system contributes to the gap in educational achievement between rich and poor.