I wouldn't put that orbitals are one-electron functions. HOMO is usually occupied by an electron pair, and is stationary. But considering these two electrons independently of the others is an approximation, fully agreed.
The Slater determinant is not precisely the total wave function, as this process neglects the forces between the electrons. Slater is only a step after the Hartree-Fock approximation, which lacks accuracy for taking individual electrons that don't interact. This misses the shielding effect for instance, or if shielding by "deeper" shells is introduced in the model, it misses more subtle but consequent effects.