Chris,
From Mamiya America;
Q. May I use 120 film in a 220 back and vice-versa?
A. Do this only in an emergency. The pressure plates of the two backs are slightly different to allow for the presence/lack of paper backing. The difference in the film plane may cause focus problems at wide apertures. Squeezing 120 film and paper through 220 rollers designed for film only will strain the back’s advance mechanism. Also, the 120 back’s counter will release after exposure #10 and waste the second half of a 220 roll. The 220 back’s counter will continue past #10, running the risk of shooting on the leader paper if strict attention is not paid to the counter.
From my own experience;
Putting 120 in a 220 back does make it harder to wind between exposures. Also the extra thickness of 120 can over time weaken the pressure plate spring. What happens then is when you use 220 in the back the vacuum produced behind the mirror, when it flips up, will pull the film out of the plane of focus, creating a very slight softness in the image. Rebuilding the backs with new springs cured the softness.
HTH
Rich