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.
