The interaction of error fields with a system of differentially rotating conducting walls is studied analytically and compared to experimental data. Wall rotation causes eddy currents to persist indefinitely, attenuating and rotating the original error field. Superposition of error fields from external coils and plasma currents are found to break the symmetry in wall rotation direction. The vacuum and plasma eigenmodes are modified by wall rotation, with the error field penetration time decreased and the kink instability stabilized, respectively. Wall rotation is also predicted to reduce error field amplification by the marginally stable plasma.