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 ~ 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.
