As a straightforward application of the recently calculated two-loop heavy quarkonium Hamiltonian, we evaluate the two-loop <math><mi>O</mi><mo>(</mo><mi>ϵ</mi><mo>)</mo></math> term of the <math><mn>1</mn><mo>/</mo><mo>(</mo><mi>m</mi><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math> heavy quarkonium potential. Compared to a previous calculation we find a small difference in the coefficient of the maximally non-abelian color factor <math><msub><mrow><mi>C</mi></mrow><mrow><mi>F</mi></mrow></msub><msubsup><mrow><mi>C</mi></mrow><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math>. We further examine this coefficient carefully.