We present results of two dimensional (2D) and three dimensional (3D) calculations for dissociative and diffractive scattering of H-2 from Pt(111), using a potential energy surface obtained from density functional theory (DFT) employing the generalized gradient approximation (GGA) in conjunction with a slab representation of the metal surface. The present study is motivated by the importance of Pt as a hydrogenation catalyst, and by a paradox regarding the amount of corrugation of the H-2+Pt(111) potential energy surface (PES). Molecular beam experiments on dissociation of D-2 from a Pt(111) surface suggest a rather corrugated PES, which is at odds with results from molecular beam experiments on rotationally inelastic diffraction of HD from Pt(111), where only very little diffraction is found, suggesting a weakly corrugated PES. Results of our 3D calculations for off-normal incidence show that the present 3D model does not obey normal energy scaling, and that parallel motion inhibits dissociation at low collision energies, in agreement with the dissociation experiment. On the other hand, substantial diffraction is found, where the diffraction experiment found almost none. For each impact site considered in the 2D calculations, the computed dynamical barrier height, E-0, is substantially lower than the barrier height in the PES, E-b, at that site. Both the 2D and the 3D calculations show a large vibrational enhancement of reaction. These effects are not due to a reduced mass effect, the barrier to dissociation being early, but to a decrease in the force constant of the H-2 vibration upon approaching the barrier to dissociative adsorption from the gas phase. The vibrational enhancement computed for H-2+Pt(111) was not observed in seeded beam experiments on D-2+Pt(111) [A. C. Luntz, J. K. Brown, and M. D. Williams, J. Chem. Phys. 93, 5240 (1990)]. However, an analysis performed here strongly suggests that seeded beam experiments will be unable to observe vibrational enhancement if the dissociation of the molecule in nu =0 proceeds without an energetic threshold, as is the case for H-2+Pt(111).