The N-methylacetamide molecule (NMA) is an important model for peptide and protein vibrational spectroscopy as it contains the main amide chromophore. In the past, some observed NMA geometry and spectral features could not be entirely explained at the harmonic level or by a single-conformer model. In particular, the spectra were found to be very dependent on molecular environment. In this work NMA Raman and infrared (IR) spectra in a variety of conditions were remeasured and simulated theoretically to separate the fundamental, dimer, and anharmonic bands. Under vacuum the MP2, MP4, and CCSD(T) wave function methods predicted a broad anharmonic potential energy well or even a double-well for the amide nitrogen out of plane motion, which density functional methods failed to reproduce. However, eventual nonplanar minima cannot Support an asymmetric quantum state or explain band splittings observed in some experiments. In polar solvents the potential becomes more harmonic and the amide plane more rigid. On the other hand, solvent polarity enhances other anharmonic phenomena, such as the coupling between the carbonyl stretching (amide I) and lower frequency amide bending modes. The amide I band splitting is commonly observed experimentally. The influence of the CH3 group rotations modeled by a rigid rotor model was found to be important for explaining some features of the spectra in a solid parahydrogen matrix. At room temperature the methyl rotation contributes to a nonspecific inhomogeneous band broadening. The dependence of the amide group flexibility oil the environment polarity may have interesting consequences for peptide and protein folding Studies.