  New effects of nontrivial neutrino electromagnetic properties are
investigated on the basis of exact solutions of the modified Dirac equations
for neutrinos in dense magnetized rotating matter. The effect of spatial
separation of different types of neutrinos and antineutrinos (different in
flavors and energies) moving inside dense magnetized rotating matter is
predicted. We also describe a new mechanism of a star rotation frequency shift
by neutrinos escaping the star (termed "Neutrino Star Turning" mechanism, $\nu
S T$). The $\nu S T$ mechanism can explain the origin of pulsar "anti-glitches"
and ordinary glitches as well. Considering a possible effect of the $\nu S T$
mechanism on speeding up of a pulsar together with the observational data on
pulsars, we obtain a new limit on a neutrino millicharge
$q_{\nu}<1.3\times10^{-19}e_0$ that is one of the strongest limits on this
value obtained in astrophysics.
