  The derivation of effective quantum gravity corrections to Newton's potential
is an important step in the whole effective quantum field theory approach. We
hereby add new strong arguments in favor of omitting all the diagrams with
internal lines of the massive sources, and we also recalculate the corrections
to the Newtonian potential using functional methods in an arbitrary
parametrization of the quantum fluctuations of the metric. The general proof of
the gauge- and parametrization-independence within this approach is also
explicitly given. On top of that, we argue that the universality of the result
holds regardless of the details of the ultraviolet completion of quantum
gravity theory. Indeed, it turns out that the logarithm quantum correction
depends only on the low energy spectrum of the theory that is responsible for
the analytic properties of loop's amplitudes.
