From a spectroscopic survey of candidate H ii regions in the Andromeda Galaxy (M31) with MMT/Hectospec, we have identified 294 H ii regions using emission line ratios and calculated elemental abundances from strong-line diagnostics (values ranging from subsolar to supersolar) producing both oxygen and nitrogen radial abundance gradients. The oxygen gradient is relatively flat, while the nitrogen gradient is significantly steeper, indicating a higher N/O ratio in M31's inner regions, consistent with recent simulations of galaxy chemical evolution. No strong evidence was found of systematic galaxy-scale trends beyond the radial gradient. After subtracting the radial gradient from abundance values, we find an apparently stochastic and statistically significant scatter of standard deviation 0.06dex, which exceeds measurement uncertainties. One explanation includes a possible collision with M32 200-800Myr ago. Using the two-point correlation function of the oxygen abundance, we find that, similar to other spiral galaxies, M31 is well-mixed on sub-kpc scales but less so on larger (kpc) scales, which could be a result of an exponential decrease in mixing speed with spatial scale, and the aforementioned recent merger. Finally, the MMT spectroscopy is complemented by a dust continuum and CO survey of individual giant molecular clouds, conducted with the Submillimeter Array (SMA). By combining the MMT and SMA observations, we obtain a unique direct test of the oxygen abundance dependence of the {alpha}'(^12^CO) factor which is crucial to convert CO emission to dust mass. Our results suggest that within our sample there is no trend of the {alpha}'(^12^CO) with oxygen abundance.