We include the full second-order corrections to the static QCD potential in the analysis of the tt̄ 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 theoritical uncertainties of the QCD potential in relation to the tt̄ threshold cross section. In particular there exists a theoritical uncertainty which limits our present theoritical accuracy of the tt̄ threshold cross section at the peak to be δσpeak/σpeak≳6% within perturbative QCD.