What are the efficiency limits of the Peltier effect?
The Peltier effect happens between two junctions of electrically conductive materials with different atomic lattice structures. Flow of current creates temperature difference between two junctions, but also generated the Joule heat in conductors. Also the link between two junctions is thermally conductive. So the thermolelectric element efficiency is limited by thermal "short" from cooled surface to hot surface and parasitic heat from dissipation in conductors. To increase element efficiency (aka "figure of merit", zT) the thermal conductance needs to be minimized, while electrical conductivity increased. 

Unfortunately, Physics of thermal conductivity and electrical conductivity is bounded to the same internal mechanism - collective oscillations of atomic lattice, or phonons. Scholars figured out that the thermal conductivity has bottom limit for amorphous state of materials, which, unfortunately, has the lowest electrical conductivity. So the efficiency requirements for thermoelectric elements are inherently contradictory, and there is only so much one can do to improve the situation with band structure engineering using additions of different impurities.