X-ray burst model predictions of light curves and the final composition of the nuclear ashes are affected by uncertain nuclear masses. However, not all of these masses are determined experimentally with sufficient accuracy. Here we identify the remaining nuclear mass uncertainties in X-ray burst models using a one-zone model that takes into account the changes in temperature and density evolution caused by changes in the nuclear physics. Two types of bursts are investigated-a typical mixed H/He burst with a limited rapid proton capture process (rp-process) and an extreme mixed H/He burst with an extended rp-process. When allowing for a 3{sigma} variation, only three remaining nuclear mass uncertainties affect the light-curve predictions of a typical H/He burst (^27^P, ^61^Ga, and ^65^As), and only three additional masses affect the composition strongly (^80^Zr, ^81^Zr, and ^82^Nb). A larger number of mass uncertainties remain to be addressed for the extreme H/He burst, with the most important being ^58^Zn, ^61^Ga, ^62^Ge, ^65^As, ^66^Se, ^78^Y, ^79^Y, ^79^Zr, ^80^Zr, ^81^Zr, ^82^Zr, ^82^Nb, ^83^Nb, ^86^Tc, ^91^Rh, ^95^Ag, ^98^Cd, ^99^In, ^100^In, and ^101^In. The smallest mass uncertainty that still impacts composition significantly when varied by 3{sigma} is ^85^Mo with 16keV uncertainty. For one of the identified masses, ^27^P, we use the isobaric mass multiplet equation to improve the mass uncertainty, obtaining an atomic mass excess of -716(7)keV. The results provide a roadmap for future experiments at advanced rare isotope beam facilities, where all the identified nuclides are expected to be within reach for precision mass measurements.