With the example of the (4 2) commensurate phase of CO adsorbed on MgO(100) below 40 K, we illustrate the difficulty for determining the adsorption sites and the orientations of the admolecules. This system takes advantage of abundant experimental information issued from electron and helium diffraction patterns and infrared signals, and from a lot of theoretical calculations including ab initio approaches as well as semi-classical atom-atom methods. However, due to the specific arrangement of the molecules along the Mg troughs of the substrate, a lot of orientational configurations for the molecules in the unit cell correspond to very close adsorption energy values and no configuration perfectly fits the whole set of experimental data. We thus consider the features which can be at the origin of such a discrepancy.