  We present a catalog of 74 galaxies detected serendipitously during a
campaign of spectroscopic observations of the Hubble Deep Field North (HDF) and
its environs. Among the identified objects are five candidate Ly-alpha emitters
at z > 5, a galaxy cluster at z = 0.85, and a Chandra source with a heretofore
undetermined redshift of z = 2.011. We report redshifts for 25 galaxies in the
central HDF, 13 of which had no prior published spectroscopic redshift. Of the
remaining 49 galaxies, 30 are located in the single-orbit HDF Flanking Fields.
We discuss the redshift distribution of the serendipitous sample, which
contains galaxies in the range 0.10 < z < 5.77 with a median redshift of z =
0.85, and we present strong evidence for redshift clustering. By comparing our
spectroscopic redshifts to optical/IR photometric studies of the HDF, we find
that photometric redshifts are in most cases capable of producing reasonable
predictions of galaxy redshifts. Finally, we estimate the line-of-sight
velocity dispersion and the corresponding mass and expected X-ray luminosity of
the galaxy cluster, we present strong arguments for interpreting the Chandra
source as an obscured AGN, and we discuss in detail the spectrum of one of the
candidate z > 5 Ly-alpha emitters.
