50 Hz noise only in chest leads of 12 lead ECG
Use of the Wilson Central Terminal can cause noisy recordings.  (Stevenson, William G., and Kyoko Soejima. "Recording techniques for clinical electrophysiology." Journal of cardiovascular electrophysiology 16.9 (2005): 1017-1022.)  All biopotential amps are somewhat differential, but to get the unipolar leads, the second side is effectively ground, and so you have a lower CMRR.  It can simply come down to differential vs pseudo-differential

See also "Wan, Sunny WS, and Hung T. Nguyen. "50 Hz interference and noise in ECG recordings—A review." Aust. Phys. Eng. Sci. Med 17 (1994): 108-115."

It's also possible that your electrodes are not all well placed.  Have you tried abrading the skin lightly?  Are you using driven leg techniques, which can  reduce effective electrode impedance?  A complete diagram, including the types of electrodes you are using would be of help.