The only failure mode of which I am aware is an overtorque situation, where the magnetic coupling 'slips a pole' (actually two). In small magdrive pumps, it produces some acoustic noise.
If you're talking about a pump driven by a wetted magnet, as far as I know the principal modes of failure are dry run (even very brief dry run) which leads to failure of the ceramic bearings/bushings the instant they are hit with cold liquid, or debris/solids leading to plugging of the flow passages between the magnet and outer "can" which leads to overheating and failure of the bearings/bushings or the magnet itself.