Magneto-optical imaging was used to visualize the inhomogeneous penetration of magnetic flux into polycrystalline TlBa2Ca2Cu3Ox films with high critical current densities, to reconstruct the local two-dimensional supercurrent flow patterns and to correlate inhomogeneities in this flow with the local crystallographic misorientation. The films have almost perfect c-axis alignment and considerable local a- and b-axis texture because the grains lend to form colonies with only slightly misaligned a and b axes, Current flows freely over these low-angle grain boundaries but is strongly reduced at intermittent colony boundaries of high misorientation, The local (<10-micrometer scale) critical current density J(c) varies widely, being up to 10 times as great as the transport J(c) (scale of similar to 1 millimeter), which itself varies by a factor of about 5 in different sections of the film, The combined experiments show that the magnitude of the transport J(c) is largely determined by a few high-angle boundaries.