We present a study of photometric redshift accuracy in the 3D-HST photometric catalogs, using 3D-HST grism redshifts to quantify and dissect trends in redshift accuracy for galaxies brighter than $H_{F140W}<24$ with an unprecedented and representative high-redshift galaxy sample. We find an average scatter of $0.0197pm0.0003(1+z)$ in the Skelton et al. (2014) photometric redshifts. Photometric redshift accuracy decreases with magnitude and redshift, but does not vary monotonically with color or stellar mass. The 1-$sigma$ scatter lies between $0.01-0.03$(1+z) for galaxies of all masses and colors below $z<2.5$ (for $H_{F140W}{<}24$), with the exception of a population of very red ($U-V > 2$), dusty star-forming galaxies for which the scatter increases to $sim0.1(1+z)$. Although the overall photometric redshift accuracy for quiescent galaxies is better than for star-forming galaxies, scatter depends more strongly on magnitude and redshift than on galaxy type. We verify these trends using the redshift distributions of close pairs and extend the analysis to fainter objects, where photometric redshift errors further increase to $sim0.046(1+z)$ at $H_{F160W}=26$. We demonstrate that photometric redshift accuracy is strongly filter-dependent and quantify the contribution of multiple filter combinations. We evaluate the widths of redshift probability distribution functions and find that error estimates are underestimated by a factor of $sim1.1-1.6$, but that uniformly broadening the distribution does not adequately account for fitting outliers. Finally, we suggest possible applications of these data in planning for current and future surveys and simulate photometric redshift performance in the LSST, DES, and combined DES and VHS surveys.
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