  A variety of subtle, and not-so-subtle selection effects influence the
interpretation of galaxy counts, sizes and redshift distributions in the Hubble
Deep Field. Comparison of the different HDF catalogs available in the
literature and on the world-wide-web reveals generally good agreement, although
the effects of different isophotal thresholds and different splitting
algorithms are readily apparent. As the basic source detection and photometry
algorithms are similar for the different catalogs, the selection effects are
likely to affect them all. Through simulations, we explore the utility of image
moments for inferring the true sizes of galaxies. The truncation of galaxy
profiles at a fixed isophote has serious consequences, which limit constraints
on the size distribution to galaxies with isophotal magnitudes I < 27.5.
Present-day L* spirals would be undetected in the HDF above redshifts z ~ 1.2,
and present-day ellipticals would disappear at z ~ 1.8. The Lyman break
provides a way to identify high-redshift galaxies at very faint magnitudes.
However, galaxies that are at redshifts high enough to vanish from the HDF
F300W or F450W filters also suffer severely from photometric biases. For
example, at fixed total apparent magnitude and physical scale length, a galaxy
at z=4 will have a mean surface brightness 1.2 mag fainter than a galaxy at
z=2.75. This lower surface brightness will result in an apparent decrease in
the number density of objects, and the inferred luminosity density, even for
models where there is no intrinsic evolution. We illustrate the effects of
these biases on the estimates of the number of Lyman ``dropouts'' in the HDF
and on the luminosity density at z > 2.
