We include the full second-order corrections to the
static QCD potential in the analysis of the $t\bar{t}$
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 $t\bar{t}$ threshold cross section.
In particular there exists a theoretical uncertainty which limits our present
theoretical accuracy of the $t\bar{t}$
threshold cross section at the peak to be
$\delta \sigma_peak/\sigma_peak \simgt 6\%$
within perturbative QCD.
