  We report the first uniform and systematic study of dust and molecular gas in
nearby molecular clouds. We use surveys of dust extinction and emission to
determine the opacity and map the distribution of the dust within a dozen local
clouds in order to derive a uniform set of basic cloud properties. We find: 1)
the average dust opacity $\langle\kappa_{d,353}\rangle = 0.8\ {\rm cm^{2}\,
g^{-1}}$ with variations of a factor of $\sim$ 2 between clouds, 2) cloud PDFs
are exquisitely described by steeply falling power-laws with a narrow range of
slope, and 3) a tight $M_{\rm GMC} \sim R_{\rm GMC}^2$ scaling relation for the
cloud sample, indicative of a cloud population with an exactingly constant
average surface density above a common fixed boundary. We compare these results
to uniformly analyzed CO surveys. We measure the CO mass conversion factors and
assess the efficacy of CO for tracing the physical properties of molecular
clouds. We find $\langle \alpha_{\rm CO}\rangle = 4.31 \pm 0.67$ M$_\odot$ (K
km s$^{-1}$ pc$^2$)$^{-1}$ (corresponding to $X_{\rm CO}$ = 1.97 $\times$
10$^{20}$ cm$^{-2}$(K km s$^{-1}$)$^{-1}$). We demonstrate that CO observations
are a poor tracer of column density and structure on sub-cloud spatial scales.
On cloud scales, CO observations can provide measurements consistent with those
of the dust, provided data are analyzed in a similar, self-consistent fashion.
Measurements of average GMC surface density are sensitive to choice of cloud
boundary. Care must be exercised to adopt common fixed boundaries when
comparing surface densities for cloud populations within and between galaxies.
