We present new imaging at 12.81 and 11.7 microns of the central ~40x30 (~0.7x0.5 kpc) of the starburst galaxy M82. The observations were carried out with the COMICS mid-infrared (mid-IR) imager on the 8.2m Subaru telescope, and are diffraction-limited at an angular resolution of <0.4. The images show extensive diffuse structures, including a 7-long linear chimney-like feature and another resembling the edges of a ruptured bubble. This is the clearest view to date of the base of the kpc-scale dusty wind known in this galaxy. These structures do not extrapolate to a single central point, implying multiple ejection sites for the dust. In general, the distribution of dust probed in the mid-IR anticorrelates with the locations of massive star clusters that appear in the near-infrared. The 10-21 micron mid-IR emission, spatially-integrated over the field of view, may be represented by hot dust with temperature of ~160 K. Most discrete sources are found to have extended morphologies. Several radio HII regions are identified for the first time in the mid-IR. The only potential radio supernova remnant to have a mid-IR counterpart is a source which has previously also been suggested to be a weak active galactic nucleus. This source has an X-ray counterpart in Chandra data which appears prominently above 3 keV and is best described as a hot (~2.6 keV) absorbed thermal plasma with a 6.7 keV Fe K emission line, in addition to a weaker and cooler thermal component. The mid-IR detection is consistent with the presence of strong [NeII]12.81um line emission. The broad-band source properties are complex, but the X-ray spectra do not support the active galactic nucleus hypothesis. We discuss possible interpretations regarding the nature of this source.