The problems with BMI include:
1. It takes no account of the muscular composition of the body (or indeed bones structure)
2. As height increases, the amount of non fat mass (bones, muscles, water etc) increase by a greater proportion, so BMI is particularly inaccurate for tall (or short) people
3. From the perspective of heart health, visceral (around the organs) fat is much more important than weight so BMI is not as good a measure of cardiovascular risk a waist measurement (or waist: hip ratio) because it cannot differentiate between visceral and subcutaneous (under the skin) fat.
There may be more but I don't know. Personally, I have always thought that because I have short legs and a long body, I should be given a little more leeway!