We use a perturbation technique to compute the rotational corrections to the non-radial oscillation spectrum of a realistic neutron-star model. We compute, to first order in the rotation rate, the corrections to the normal mode eigenfrequencies and eigenfunctions. We find that l = l0 oscillations are coupled to l = l0 ± 1 oscillations by the Coriolis force. For the toroidal modes, this coupling introduces a non-zero radial component to the velocity field. We have used this result to compute the neutrino damping rates for several corrected toroidal modes. This damping mechanism is inoperative for toroidal modes in a non-rotating star because these modes produce no density nor temperature perturbations. The neutrino damping time can approach the gravitational radiation damping time in rotating neutron stars if the central temperature is high enough, (Tc ≥ 108 K). The rotationally induced coupling of spheroidal oscillations to toroidal modes can also produce significant displacements at the stellar surface. This may have interesting implications for channeling energy, e.g., that associated with a glitch, to the surface of the star. Perhaps this might produce observable effects in the pulsar emission process or a γ-ray burst event.