  [Abridged] We examine the physical properties of 173 cluster members in
CL1358+62 (z=0.33) from HST WFPC2 imaging taken in the F606W & F814W filters
(rest-frame B & V) over a 2.2x2.2 Mpc^2 field. Structural parameters are
measured for each member by fitting a PSF-convolved, two component model to
their 2D surface brightness distribution. We examine bulge+disk models using
three different bulge profiles (de Vaucouleurs, Sersic, and exponential), and
rigorously test the robustness of our results by analyzing several thousand
artificial galaxies in the same manner as the cluster data. Combining
structural parameters with ground-based spectroscopy, we test for correlations
between morphological characteristics, current star formation, total galaxy
colors, and cluster substructure. We find that: (1) Using a de Vaucouleurs
bulge, bulge-to-total ratios and Hubble type (-5<T<8) are strongly correlated
(99% CL), but the scatter is large and early-type spirals are not reliably
distinguished from E's and S0's based on (B/T). (2) The low luminosity
ellipticals in our sample are likely to be face-on S0 galaxies. (3) High galaxy
asymmetry and strong [OII] emission are strongly correlated for disk-dominated
members. (4) There exists a small population (~5%) of bulge-dominated members
whose significant [OII] emission (<-5A) suggest they harbor AGN. (5) At these
redshifts, determining the correct Sersic index can be highly unreliable.
