We present 1.644 μm [Fe II] and 1.570 μm continuum images of the Crab Nebula which are compared with optical Hα, [O III], and 5100 Å continuum data. While the same prominent filaments are generally apparent in all lines, we find substantial variations within the nebula in the strength and morphology of [Fe II] relative to the other lines. The [Fe II] image appears to be virtually identical to the [Ni II] image published by MacAlpine et al. in 1989, indicating that the gas phase distributions of Fe+ and Ni+ are very similar. Our data indicate that the solution to the "Ni/Fe problem" probably lies in errors in the atomic data used to calculate line strengths in [Ni II]. Observed variations in filament spectra may be primarily due to differences in filament structure rather than abundances; current filament models are inadequate to reliably distinguish between these effects. In particular, variations in column depth and confinement by magnetic fields can lead to significant differences in the relative prominence of lines formed in the H0, H+ → H0, and H+ zones. The only spatial variations in abundance which we believe can be inferred with confidence at this time is an enhancement in the abundance of H in the northern part of the nebula. The infrared to optical continuum ratio of the synchrotron nebula shows ∼ 15%-20% variations which are dominated by features which appear related to the position of the pulsar. We interpret these as variations of ∼ 0.15 in the spectral index and suggest they are related to the radiative decay of energetic particles and the paths over which these particles travel from the pulsar throughout the nebula. There are a number of small-scale features in the continuum ratio map that are associated with prominent emission-line filaments. These are interpreted as extinction due to dust in the filaments, a result consistent with other reports of dust in the Crab.