Density functional theory (DFT) has provided many insights into the freezing of simple fluids. Several analytical and numerical solution have shown that the DFT provides an accurate description of freezing of hard spheres and their mixtures. Compared to other techniques, numerical, grid-based algorithms for solving the DFT equations have more variational freedom and are capable of describing subtle behavior, as that seen in mixtures with multipeaked density profiles. However the grid-based approach is sensitive to the coarseness of the mesh employed. Here we summarize how the granularity of the mesh affects the freezing point within the DFT. For coarse meshes, we show that the freezing point is masked by numerically induced false minima of the DFT grand potential. These false minima are removed when a fine enough grid is used to represent properly the density profiles. Our results suggest that others using such grid-based methods have focused on such numerical artifacts that have little to do with real phenomena.