The rate of impact excitation of each of the free motions of the moon above a given amplitude is compared with the rate of damping from tidal and rotational distortion and from a possible core-mantle interaction. Criteria are developed in terms of the damping factor Q and the core kinematic viscosity &ngr; for which each amplitude should be expected to be above the projected observational limit of 0.01 arc sec determined by the laser ranging and very long base line interferometry experiments. Although observable amplitudes are compatible with reasonable values of Q and &ngr;, it is also not unreasonable for the amplitudes to be below observability most of the time. Of the three free motions the libration in longitude is the least likely to be observable in spite of its more frequent excitation, and amplitudes of this motion as high as 1.0 arc sec must be regarded as very unlikely. A tentatively identified liquid core of 270-km radius might keep some of the motions damped below observability if &ngr; is well within the bounds estimated for the earth's core, but it probably could not keep all of them so damped. Within a given model the uncertainty in the expectation of observable free motions rests on the uncertainty in the values of Q and &ngr;, where the latter includes the possibility of no liquid core at all. Uncertainties in the various assumptions incorporated into the models themselves are discussed explicitly. The detection of any free motions may bound values of some of the parameters and thus yield information about the lunar interior.