A molecular dynamics simulation study of the SPC/E model for water is reported in which three systems representing liquid H2O, D2O, and T2O are compared at 25 degrees C. One of our principal aims is to systematically examine kinetic isotope effects in a simple water model. We have investigated the translational dynamics by focusing upon the principal components of the translations self-diffusion coefficients; the out-of-plane displacements of water molecules (as measured by their translational diffusion) demonstrate the largest isotopic effects. We also compare the single-molecule rotational correlation times and the collective dielectric relaxation times. Our simulation results clearly indicate that the orientational dynamics of the molecular dipoles in liquid SPC/E water are weakly affected by rototranslational coupling. Thus, ratios of single-dipole self-times (tau(1)/tau(2)) in liquid H2O, D2O, and T2O are only slightly smaller than their ideal (Debye) value of 3. At the same time, large deviations from Debye behavior are observed in the orientational motion of the molecular axes orthogonal the dipolar axis.