Possible sources of residual errors in the theoretical energies of the hydrogen molecule are investigated. Nonadiabatic corrections are computed for all bound, J less than or equal to 10 X 1 Sigma(g) (+) ro-vibrational states of the six isotopic hydrogen molecules. The new results improve significantly the overall agreement with accurate experimental transition frequencies. In order to estimate the convergence errors of the Born-Oppenheimer energies generalized James-Coolid,ae functions with powers of the interelectronic distance, r(12), up to 6 are used and the precision of the computations is increased. Except for the equilibrium separation, R =1.4011 bohr, the obtained potential energy curve is lower by a few thousandths of a wave number than any other reported variational result. This lowers the v=0 vibrational levels by 0.009 cm(-1) and results in a dissociation energy of H-2, D-0=36118.069 cm(-1).