Recently, analysis of the optical counterpart AT2017gfo to the gravitational wave-detected neutron star merger GW170817 has suggested a promising resolution of a long-standing debate on neutron star mergers as a source of some of the heaviest elements. However, making quantitative progress in these areas requires an accounting of the uncertainties in different aspects of physics, which is input into simulations of merging compact objects and their associated phenomena, remarkably rapid neutron capture nucleosynthesis. We investigate the uncertainties from the nuclear inputs to rapid neutron capture nucleosynthesis calculations combining different theoretical nuclear mass models, spontaneous fission rates, and fission daughter product distributions on top of the experimental nuclear data. We report that such nuclear physics uncertainties typically generate at least one order of magnitude uncertainty in the nuclear heating, which leads to uncertainties in the bolometric luminosity and the inferred mass of r-process material from the kilonova light curve.