The nearby grand-design spiral galaxy M51 (NGC 5194), which is viewed almost face-on, is ideal for studying molecular gas properties, physical conditions and star formation processes at high spatial resolution with single-dish telescopes. I will present the first complete CO J=3-2 map of M51 at sub-kiloparsec spatial resolution and covering the entire optical galaxy disk, which was obtained with the HARP-B instrument on the James Clerk Maxwell Telescope. I will describe the comparison of the HARP-B CO J=3-2 integrated intensity map with maps of CO J=2-1, CO J=1-0 and other data from the literature. I will then discuss our investigation of the variation of the molecular gas, atomic gas and polycyclic aromatic hydrocarbon (PAH) properties of M51 as a function of distance along the spiral structure on sub-kiloparsec scales, in particular comparing differences and similarities between properties such as CO line ratios in the spiral arms and inter-arm regions.