Magnetic properties of highly zinc-substituted manganese ferrites are discussed on the basis of cation distribution. High throughput neutron powder diffractometry indicates that the prepared samples possess a nearly normal spinel structure, where the substitution of nonmagnetic zinc ions mainly causes the dilution of magnetic ions in the A-sublattice and consequently affects bond-randomness in the B-sublattice. On the other hand, the estimated occupancy of manganese ions in the B site indicates that random anisotropy effects due to local Jahn-Teller distortions gradually weaken with the substitution. Bulk magnetometry indicates that the substitution smears the transition from a paramagnetic phase to a soft-magnetic phase. Furthermore, at lower temperatures, such a soft-magnetic phase is destabilized and a magnetic glassy state appears. These features of the magnetic properties of dilute spinel ferrites are discussed from the viewpoint of the above-mentioned various types of disorders.