We study experimentally the influence of the transverse dimension on film flow in relatively wide channels with sidewalls. Large deviations from two-dimensional predictions are observed in the primary instability and in the post-threshold traveling waves, and the deviations are presently shown to depend strongly on fluid physical properties. Measurements for a wide range of fluid properties are found to correlate with the Kapitza number, which represents the ratio of capillary to viscous stresses. These observations point to an unexpected long-range effect of surface tension that provides transverse coherence to the flow.