Growing interest in high precision studies of the Earth's gravitational field warrant a critical review of precision requirements to yield useful results. Several problems are now under consideration. All of these problems involve, more or less, the precise value of the vertical gradients of gravity. The principle conclusion from this review is that the essential absence of Free Air Vertical Gravity Gradient control and actual values of gravimeter calibrations require serious attention. Large errors in high topography on official published gravity maps also cannot be ignored.