We find that disk galaxies show a sharp, mass-dependent transition in the structure of their dusty ISM. Dust lanes are a generic feature of massive disks with V_rot>120km/s, but are completely absent in galaxies with V_rot<120km/s. The transition reflects an increase in the scale height of the cold ISM in low mass galaxies, driven by larger turbulent velocities supporting the gas layer, rather than sharp drops in the gas surface density. We identify the V_rot=120km/s transition with the onset of gravitational instabilities in high mass galaxies. The instabilities lead to fragmentation and gravitational collapse along spiral arms, smaller gas scale heights, lower turbulent velocities, and thus to narrow dust lanes. The drop in velocity dispersion may be due either to a switch in the driving mechanism for turbulence or to a change in the response of the ISM to supernovae after the ISM has collapsed to a dense layer. The resulting smaller gas scale height can lead to significant increases in the star formation rate when disk instabilities are present, and may explain the Kennicutt surface density threshold for star formation. Our data suggest that star formation will be systematically less efficient in low mass disks with V_c<120km/s, leading to star formation timescales longer than the gas accretion timescale. This effect can suppress the metallicity and nucleosynthetic yields of low mass disks, and thus explain the disk mass-metallicity relationship without invoking galactic SN-driven outflows. The transitions in disk stability, dust structure, and/or star formation efficiency may also be responsible for observed changes in the slope of the Tully-Fisher relation, in the sharp increase in the thickness of dwarf galaxy disks, and in the onset of bulges in galaxies with V_rot>120km/s. (Abridged)
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