  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 $0.0197\pm0.0003(1+z)$ 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.
