Magnetic field mapping of three H I features, toward MBM 12, MBM 40, and H0928+02, was attempted using 21 cm Zeeman effect observations corrected for sidelobe signals. A detailed description of errors introduced into the observations through interaction between H I brightness structure around the source direction and polarized beam structure is given. After corrections were applied to the data, no unambiguous magnetic field effects were found. The previous claim by this author of a held toward NPS 20, associated with MBM 40, is not confirmed. For each mapped area the individual held fits were averaged, and the results indicate 0.25+/-0.12 mu G for the MBM 40 region (error 1 sigma), 0.48+/-0.31 mu G for H0928+02, and -0.29+/0.38 mu G for those directions toward MBM 12 where the data were judged to be reliable. The implied upper limits of 0.36 mu G for the MBM 40 region and less than 1.0 mu G for the other two suggest that the magnetic field strength in diffuse H I observed with a 22' beam is far lower than has heretofore been recognized.