  We include the full second-order corrections to the static QCD potential in
the analysis of the ttbar threshold cross section. Then we examine the
difference between the results obtained in the momentum-space approach and in
the coordinate-space approach, which was found recently. Contrary to our
expectation, the reduction of the difference by the inclusion of the
second-order corrections is very small. There still remains a non-negligible
deviation, which originates from the difference in the construction of the
potentials in the two spaces. We scrutinize this problem. In particular, we
estimate our present theoretical uncertainty of the ttbar threshold cross
section at the peak to be at least 6% within perturbative QCD.
