The Plateau de Bure Interferometer Arcsecond Whirlpool Survey has mapped the molecular gas in the central ~9 kpc of M51 in its 12CO(1-0) line emission at a cloud-scale resolution of ~40 pc using both IRAM telescopes. We utilize this data set to quantitatively characterize the relation of molecular gas (or CO emission) to other tracers of the interstellar medium, star formation, and stellar populations of varying ages. Using two-dimensional maps, a polar cross-correlation technique and pixel-by-pixel diagrams, we find: (1) that (as expected) the distribution of the molecular gas can be linked to different components of the gravitational potential; (2) evidence for a physical link between CO line emission and radio continuum that seems not to be caused by massive stars, but rather depends on the gas density; (3) a close spatial relation between polycyclic aromatic hydrocarbon (PAH) and molecular gas emission, but no predictive power of PAH emission for the molecular gas mass; (4) that the I - H color map is an excellent predictor of the distribution (and to a lesser degree, the brightness) of CO emission; and (5) that the impact of massive (UV-intense) young star-forming regions on the bulk of the molecular gas in central ~9 kpc cannot be significant due to a complex spatial relation between molecular gas and star-forming regions that ranges from cospatial to spatially offset to absent. The last point, in particular, highlights the importance of galactic environment--and thus the underlying gravitational potential--for the distribution of molecular gas and star formation.