ABSTRACT We present Large Binocular Telescope observations of 109 H ii regions in NGC 5457 (M101) obtained with the Multi-Object Double Spectrograph. We have robust measurements of one or more temperature-sensitive auroral emission lines for 74 H ii regions, permitting the measurement of "direct" gas-phase abundances. Comparing the temperatures derived from the different ionic species, we find: (1) strong correlations of TN ii with TS iii and TO iii, consistent with little or no intrinsic scatter; (2) a correlation of TS iii with TO iii, but with significant intrinsic dispersion; (3) overall agreement between TN ii, TS ii, and TO ii, as expected, but with significant outliers; (4) the correlations of TN ii with TS iii and TO iii match the predictions of photoionization modeling while the correlation of TS iii with TO iii is offset from the prediction of photoionization modeling. Based on these observations, which include significantly more observations of lower excitation H ii regions, missing in many analyses, we inspect the commonly used ionization correction factors (ICFs) for unobserved ionic species and propose new empirical ICFs for S and Ar. We have discovered an unexpected population of H ii regions with a significant offset to low values in Ne/O, which defies explanation. We derive radial gradients in O/H and N/O which agree with previous studies. Our large observational database allows us to examine the dispersion in abundances, and we find intrinsic dispersions of 0.074 0.009 in O/H and 0.095 0.009 in N/O (at a given radius). We stress that this measurement of the intrinsic dispersion comes exclusively from direct abundance measurements of H ii regions in NGC 5457.