A theoretically correct breakdown of the molecular wave function into Hartree-Fock and electron correlation components leads to the identification of four parameter problems important in approximate molecular orbital theory.The effects of the intramolecular environment on isolated atom optimized atomic orbitals, the deviation of simple basis atomic orbitals from true Hartree-Fock atomic orbitals, differences made in transforming to a basis of orthogonal atomic orbitals, and the estimation of the molecular electron correlation energy are considered. Order-of-magnitude corrections are suggested for each of these problems. Comparative NDDO all electron calculations on the carbon monoxide molecule illustrate the improved results obtained. Additional information on the performance of methods more approximate than the NDDO all electron one indicates that quantitatively they leave much to be desired.