Having the HOMO higher in energy than the LUMO is not a valid ground state, and is almost certainly an artifact of the SCF optimisation attempting to force integer occupations.
You'll see in the Fermi-smeared calculation that there are two sets of two orbitals with almost the same energy. While a partial occupation isn't a legitimate physical ground state either (though it's often good enough for an intermediate optimisation step), I think it indicates that your system in the current geometry has a multiconfigurational ground state, which DFT can't model properly. Reducing the end Fermi temperature will probably move those 0.075 parts down into the lower orbitals to give you two 0.5 occupations, but to get better than that I think you're going to have to change the geometry or at least the symmetry restrictions, to break the symmetry of those two orbitals, or else use a more sophisticated method that can model the multiconfigurational character.
I'm a little concerned about the orbitals having positive energies, which could point to additional problems in your setup. Are you performing calculations on an anion, and if so, have you included augmented functions in the basis set?
