Models of the main geomagnetic field are generally represented by a scalar potential V expanded in a finite number of spherical harmonics. In the last decade such models have been derived mainly by a recursive iteration method from the field magnitude F observed by satellites in low-altitude polar orbits. Very accurate observations of F were used, but indications exist that the accuracy of models derived from them is considerably lower. One problem is that F does not always characterize V uniquely: G. E. Backus has derived a class of counterexamples in which two different choices of V correspond to the same F. It is not clear whether such ambiguity can be encountered in deriving V from F in geomagnetic surveys, but there exists a connection, owing to the fact that the counterexamples of Backus are related to the dipole field, whereas the geomagnetic field is dominated by its dipole component. If the models are recovered with a finite error (i.e., they cannot completely fit the data and consequently have a small spurious component), this connection allows the error in certain sequences of harmonic terms in V to be enhanced without unduly large effects on the fit of F to the model. Computer simulations have demonstrated this effect, producing as a result models which fit the data of F quite closely but yield much poorer fits to the direction of the magnetic vector. Possible remedies are discussed. An appendix also discusses a particular class of fields, related to the counterexamples of Backus, for which it can happen that the recursive iteration deriving V from F does not converge to the correct solution.