The equations which describe scattering of electrons by polar molecules are discussed. The criterion for the existence of a critical dipole moment which can bind an electron is introduced. The critical moments for a freely rotating dipole are shown to coincide with those already known for a fixed dipole, and a level-crossing scheme is developed. Finally the existence of well-behaved scattering solutions, corresponding physically to virtual inelastic transitions, even at supercritical moments, is demonstrated.