Calculations of fully differential cross sections for two-photon double ionization of the hydrogen molecule with photons of 30 eV are reported. The results have been obtained by using the method of exterior complex scaling, which allows one to construct essentially exact wave functions that describe the double continuum on a large, but finite, volume. The calculated cross sections are compared with those previously obtained by Colgan et al., and discrepancies are found for specific molecular orientations and electron ejection directions.