We present high spatial resolution (similar to 1 '') and moderate spectral resolution (gamma 2/Delta gamma similar or equal to 800) Pa beta and Br gamma Fabry-Perot imaging observations of the central kiloparsec of M82. These observations, in conjunction with new near-infrared broadband imaging observations, are used to examine the extinction toward the starburst region, the state of the ionized gas, and the nature of the stellar population. Enhancements in the extinction-sensitive Pa beta/Br gamma flux ratio are found to trace out the molecular lobes seen in CO, supporting the assumption that we are observing a dense torus surrounding the central stellar clusters and H II regions. Using a nonuniform foreground screen model for the Pa beta/Br gamma flux ratio, the derived extinction toward the starburst region is found to vary from A(V) similar or equal to 2 to A(V) similar or equal to 12 mag, significantly smaller than is adopted in most other studies of the stellar population in the starburst region of M82. The extinction-corrected K-magnitude in a 30 '' aperture centered on the nucleus is found to be M(K) = -22.0. This is substantially fainter than previous values adopted, amounting to as much as a reduction of a factor of similar to 3 in the intrinsic K luminosity, a difference that substantially weakens the arguments made previously for a low mass-deficient IMF for the starburst region of M82. Our recombination line images were used to estimate separately the contribution to the near-infrared continuum bandpasses from free-free and free-bound processes and the emission from dust. These sources of emission do not contribute appreciably to the total near-infrared continuum and thus it can confidently be assumed that this emission is dominated by starlight. In addition, we present narrow-band imaging observations of M82 in the 3.29 mu m unidentified dust feature. The emission is seen to be well-correlated with the Br gamma emission. The ratio of the extinction-corrected 3.29 mu m dust feature flux to extinction-corrected Br gamma flux is found to vary from 4.5 to 15 throughout most of the starburst region, with values greater than 35 near the dynamical center of the galaxy. This variation, along with other star formation diagnostics, suggests that the nucleus contains a later-type stellar population and the starburst phenomena is propagating outward. The ratio of the total far-infrared luminosity to the dereddened 3.29 mu m feature luminosity is found to be 1340 +/- 260 for M82, significantly smaller than the ratio obtained using the uncorrected 3.29 mu m feature flux (1690 +/- 200).