We have obtained a contiguous set of long-slit spectra of a shock wave in the Cygnus Loop to investigate its structure, which is far from the morphology predicted by 1D models. Proper motions from Hubble Space Telescope images combined with the known distance to the Cygnus Loop provide an accurate shock speed. Earlier analyses of shock spectra estimated the shock speed, postshock density, temperature, and elemental abundances. In this paper we determine several more shock parameters: a more accurate shock speed, ram pressure, density, compression ratio, dust destruction efficiency, magnetic field strength, and vorticity in the cooling region. From the derived shock properties we estimate the emissivities of synchrotron emission in the radio and pion decay emission in the gamma-rays. Both are consistent with the observations if we assume simple adiabatic compression of ambient cosmic-rays as in the van der Laan mechanism. We also find that, although the morphology is far from that predicted by 1D models and the line ratios vary dramatically from point to point, the average spectrum is matched reasonably well by 1D shock models with the shock speed derived from the measured proper motion. A subsequent paper will analyze the development of turbulence in the cooling zone behind the shock.