We present evidence for the diffractive processes nu_mu Fe -> mu^- D_s^+ (D_s^*+) Fe and nubar_mu Fe -> mu^+ D_s^- (D_s^*-) Fe using the Fermilab SSQT neutrino beam and the Lab E neutrino detector. We observe the neutrino trident reactions nu_mu Fe -> nu_mu mu^- mu^+ Fe and nubar_mu Fe -> nubar_mu mu^+ mu^- Fe at rates consistent with Standard Model expectations. We see no evidence for neutral-current production of J/psi via either diffractive or deep inelastic scattering mechanisms.