  We include the full second-order corrections to the static QCD potential in
the analysis of the ttbar threshold cross section. There is an unexpectedly
large difference between the QCD potential improved by the
renormalization-group equation in momentum space and the potential improved by
the renormalization-group equation in coordinate space. This difference remains
even at a fairly short distance 1/r \simeq 100 GeV and its origin can be
understood within perturbative QCD. We scrutinize the theoretical uncertainties
of the QCD potential in relation to the ttbar threshold cross section. In
particular there exists a theoretical uncertainty which limits our present
theoretical accuracy of the ttbar threshold cross section at the peak to be not
better than 6% within perturbative QCD.
