  We demonstrate that the dispersive computation of the threshold enhancements
to heavy quark vacuum polarizations is unstable. Because of the slow
convergence of the dispersion relations the result critically depends on the
intermediate energy region where the non-relativistic approximation, intrinsic
to threshold calculations, is invalid. We discuss other ambiguities precluding
a reliable calculation of the threshold contribution to the vacuum
polarizations. In the absence of a solution prudence should force one to assign
an error to the radiative corrections not far below the level of the
pertubative O($\alpha \alpha_s$) contributions. This may preclude the
extraction of the Higgs mass from precision measurements.
