Testing for Azimuthal Abundance Gradients in M101

New optical spectra of 28 H II regions in the M101 disk have been obtained, yielding 10 new detections of the [O III] λ4363 auroral line. The oxygen abundance gradient measured from these data, combined with previous observations, displays a local scatter of 0.15 ± 0.03 dex along an arc in the west side of the galaxy, compared with a smaller scatter of 0.08 ± 0.01 dex in the rest of the disk. One of the H II regions in our sample (H27) has a significantly lower oxygen abundance than surrounding nebulae at a similar galactocentric distance, while an additional, relatively nearby one (H128) was already known to have a high oxygen abundance for its position in the galaxy. These results represent marginal evidence for the existence of moderate deviations from chemical abundance homogeneity in the interstellar medium of M101. Using a variety of strong-line abundance indicators, we find no evidence for significant large-scale azimuthal variations of the oxygen abundance across the whole disk of the galaxy.