Shaking is not related to molting. Your bird could be displaying to impress you, trying to scare you away or it could be sick. If it shakes even when you are not near the cage, I would lean toward the "could be sick" theory.
Birds should see an avian vet every year for a well check up and for vaccination, so if your bird has not seen a vet, please go ahead and take your bird in for a check up.
