The temperature dependence and the exact geometry of slow molecular reorientations in imidazolium methyl sulfonate are investigated using modern one-dimensional MAS exchange spectroscopy. Earlier high-temperature studies have evidenced a fast 180degrees flip motion of the imidazole ring, which is shown here to slow on cooling and is believed to be a prototypical molecular process involved in Grotthus-type proton transport in imidazole-based proton conductors intended for fuel cell applications. It is further shown that valuable information on the relative orientations of CH and NH dipolar coupling tensors with respect to the chemical shift anisotropy tensors of the respective heteronuclei can be obtained from the MAS exchange data as well as from static C-13 and N-15 line shapes, without the necessity of performing more involved single-crystal NMR experiments. The principal axes of the CSA tensors are found to not coincide with the CH or NH bond axes, in contrast to earlier assumptions involving similar compounds. Imidazole itself is shown to be more complex than might be expected, based on its simple structure. Implications on earlier studies of pure imidazole, where ring flips were claimed to be absent, are discussed.