  We find that magnetic neutrino-electron scattering is unaffected by
oscillations for vacuum mixing of Dirac neutrinos with only diagonal moments
and for Majorana neutrinos with two flavors. For MSW mixing, these cases again
obtain, though the effective moments can depend on the neutrino energy. Thus,
e.g., the magnetic moments measured with $\bar{\nu}_e$ from a reactor and
$\nu_e$ from the Sun could be different. With minimal assumptions, we find a
new limit on $\mu_{\nu}$ using the 825-days SuperKamiokande solar neutrino
data: $|\mu_{\nu}| \le 1.5\times 10^{-10} \mu_B$ at 90% CL, comparable to the
existing reactor limit.
