Internal kinematics, length scales, and surface brightnesses have been determined for a large sample of 53 galaxies in the cluster Cl 1358+62 at z = 0.33 from Keck spectroscopy and Hubble Space Telescope WFPC2 imaging over a 1.5 h-1 × 1.5 h-1 Mpc2 field of view. These data have been used to constrain the evolution of early-type galaxies in the cluster environment. We have constructed the fundamental plane using 30 E and S0 galaxies and draw the following conclusions. The fundamental plane at z = 0.33 has the form re ∝ σ1.31±0.13I, similar to that found locally. The 1 σ intrinsic scatter about this plane is ±14% in M/LV, comparable to that observed in Coma. We conclude that, even at intermediate redshifts, E and S0 galaxies are structurally mature and homogeneous, like those observed in nearby clusters. The M/LV ratios of these early-type galaxies are offset from the Coma fundamental plane by Δ log(M/LV) = -0.13 ± 0.03 (q0 = 0.1), indicative of mild luminosity evolution in the stellar populations in the Cl 1358+62 E and S0 galaxies. This level of evolution suggests a luminosity-weighted formation epoch for the stars of z > 1. The precise redshift depends on the initial mass function and on the cosmology. The scatter about the fundamental plane is consistent with that in the color-magnitude relation, indicating that the E/S0's have a scatter in luminosity-weighted ages of 15%. We have also analyzed the M/LV ratios of galaxies of type S0/a and later. These early-type spirals follow a different plane from the E and S0 galaxies: re ∝ σ0.66±0.29I, with a scatter that is twice as large as the scatter for the E/S0's. The difference in the tilt between the plane of the spirals and the plane of the E/S0's is shown to be due to a systematic correlation of velocity dispersion with residual from the plane of the early-type galaxies. These residuals also correlate with the residuals from the color-magnitude relation. Thus for the spirals in this cluster, as well as for the three E+A galaxies in the sample, we see a systematic variation in the luminosity-weighted mean properties of the stellar populations with central velocity dispersion. If this is a relative age trend, then luminosity-weighted age is positively correlated with σ; i.e., more massive spiral galaxies have older stars on average. The residuals from the color-magnitude relation were used to correct the surface brightnesses of the early-type spirals. After this correction for age effects, these spirals fall on the fundamental plane of E/S0's. We conclude that the early-type spirals may well evolve onto the scaling relations of the old cluster members. After correcting the spirals for the systematic trend with color, their scatter about the fundamental plane does not decrease and remains twice as large as that for the E/S0's. This large scatter should be seen in a subsample of present-day cluster galaxies, if these spirals evolve into contemporary S0's, unless some unknown process reduces their scatter. The colors and M/LV ratios imply that many cluster galaxies were forming stars at least up until z ~ 0.5, but that this activity was specific to the spiral population. The E+A's will likely evolve into low-mass present-day S0 and Sa galaxies but be slightly bluer than the present-day (B-V) color-magnitude relation by ~0.08 mag, while fading to ~1 mag below L*.