Magnetization correlations in polycrystalline thin-film recording media are studied numerically via a micromagnetic cellular automaton model. Magnetization reversal processes exhibit self-organized critically with domain patterns characterized by the intergranular exchange and magnetostatic interactions. Cross-track correlation, or domain width, is shown to be only slightly dependent on the state of magnetization. Noise in magnetic recording is related to an integration of the cross-track correlation. This integrated width is shown to increase dramatically with increasing exchange coupling and only slightly with increasing magnetostatic coupling. With no exchange coupling certain values of magnetostatic coupling yield medium noise that is below that of a system with totally noninteracting grains. For uniformly magnetized media correlations in the recording direction are stationary and found to vary in length with coupling strength. Scaling laws show that noise decreases proportional to the grain area in the film plane only if there is no intergranular exchange coupling and if the film thickness is reduced in proportion to the grain planar diameter. A review of relevant noise power relations and spectral measurement analysis is given.