We analyze high angular resolution ALMA observations of the TW Hya disk to place constraints on the CO and dust properties. We present new, sensitive observations of the (CO)-C-12 J = 3 - 2 line at a spatial resolution of 8 au (0 ''. 14). The CO emission exhibits a bright inner core, a shoulder at r approximate to 70 au, and a prominent break in slope at r approximate to 90 au. Radiative transfer modeling is used to demonstrate that the emission morphology can be reasonably reproduced with a (CO)-C-12 column density profile featuring a steep decrease at r approximate to 15 au and a secondary bump peaking at r approximate to 70 au. Similar features have been identified in observations of rarer CO isotopologues, which trace heights closer to the midplane. Substructure in the underlying gas distribution or radially varying CO depletion that affects much of the disk's vertical extent may explain the shared emission features of the main CO isotopologues. We also combine archival 1.3 mm and 870 mu m continuum observations to produce a spectral index map at a spatial resolution of 2 au. The spectral index rises sharply at the continuum emission gaps at radii of 25, 41, and 47 au. This behavior suggests that the grains within the gaps are no larger than a few millimeters. Outside the continuum gaps, the low spectral index values of alpha approximate to 2 indicate either that grains up to centimeter size are present or that the bright continuum rings are marginally optically thick at millimeter wavelengths.