  We study the geometric motion of sets in the plane derived from the
homogenization of discrete ferromagnetic energies with weak inclusions. We show
that the discrete sets are composed by a `bulky' part and an external `mushy
region' composed only of weak inclusions. The relevant motion is that of the
bulky part, which asymptotically obeys to a motion by crystalline mean
curvature with a forcing term, due to the energetic contribution of the mushy
layers, and pinning effects, due to discreteness. From an analytical standpoint
it is interesting to note that the presence of the mushy layers imply only a
weak and not strong convergence of the discrete motions, so that the
convergence of the energies does not commute with the evolution. From a
mechanical standpoint it is interesting to note the geometrical similarity of
some phenomena in the cooling of binary melts.
