We present a comprehensive analysis of the structural properties and luminosities of the 23 dwarf spheroidal galaxies that fall within the footprint of the Pan-Andromeda Archaeological Survey (PAndAS). These dwarf galaxies represent the large majority of Andromeda's known satellite dwarf galaxies and cover a wide range in luminosity (-11.6<~M_V_<~-5.8 or 10^4.2^<~L<~10^6.5^L_{sun}_) and surface brightness (25.1<~{mu}_0_<~29.3mag/arcsec^2^). We confirm most previous measurements, but we find And XIX to be significantly larger than before (r_h_=3065_-935_^+1065^pc, M_V_=-10.1_-0.4_^+0.8^) and cannot derive parameters for And XXVII as it is likely not a bound stellar system. We also significantly revise downward the luminosities of And XV and And XVI, which are now M_V_~-7.5 or L~10^5^L_{sun}_. Finally, we provide the first detailed analysis of Cas II/And XXX, a fairly faint system (M_V_=-8.0_-0.3_^+0.4^) of typical size (r_h_=270+/-50pc), located in close proximity to the two bright elliptical dwarf galaxies NGC 147 and NGC 185. Combined with the set of homogeneous distances published in an earlier contribution, our analysis dutifully tracks all relevant sources of uncertainty in the determination of the properties of the dwarf galaxies from the PAndAS photometric catalog. We further publish the posterior probability distribution functions of all the parameters we fit for in the form of MCMC chains available online; these inputs should be used in any analysis that aims to remain truthful to the data and properly account for covariance between parameters.