BMI is pretty accurate for most people. Having said that you don't need a measurement to see if someone is fat!
What is 'accurate' in this context? Accurate against what? What are you comparing it against to get a measure of accuracy?
It indicates against 'normal weight' - but if the population's weight changes then the 'normal weight' changes with it doesn't it?
The normal weight may change, but the ideal healthy weight doesn't. The idea of a healthy weight is misleading, as there is more of a healthy body fat percentage. Even that's is an oversimplification, as visceral fat has far more health implications that subcutaneous fat.