Perturbations of the most general black hole states decribed by the Kerr metric have been studied by many researchers in the past decades. In many cases, such as in the works of Chandrasekhar, Detweiler, Teukolsky, Chrzanowski and Ori, the Newman-Penrose tetrad method has been employed for both the unpertyurbed quantities and for the small perurbations. In these works, a tacit assumption is initially made that all quantities belonging to the perturbed space-time, such as the spin coefficients and the Weyl spinor compontnts are of equal order of magnitude. This implies that quantities which vanish for the Kerr metric are infinitesimal and all other quantities differ in an infinitesimal term from their values in the Kerr metric. The validity of this assumption is scrutinized here by taking into account the behaviour of observable quantities under perturbations. Former work of Christian and Sachs shows how the principal null directions can be observed by the reception of light signals. We show that the smooth behaviour of principal null direcxtions under perturbations is incompatible with the notion that the components of the perturbed Weyl spinor are of like order. Hence we conclude that either the smooth behaviour of certain physical observable under perturbations must be givben up, or the basic tenet of perturbative approaches to black holes, i.e., the equality of orders of magnitude has to be abandoned.