  We study the neutrino-induced production of nuclides in explosive supernova
nucleosynthesis for progenitor stars with solar metallicity including neutrino
nucleus reactions for all nuclei with charge numbers $Z < 76$ with average
neutrino energies in agreement with modern Supernova simulations. Considering
progenitors with initial main sequence masses between 13~M$_\odot$ and
30~M$_\odot$, we find a significant production of $^{11}$B, $^{138}$La, and
$^{180}$Ta by neutrino nucleosynthesis, despite the significantly reduced
neutrino energies. The production of $^{19}$F turns out to be more sensitive to
the progenitor mass and structure than to the $\nu$ process. With our complete
set of cross sections we have identified effects of the $\nu$~process on
several stable nuclei including $^{33}$S, $^{40}$Ar, $^{41}$K, $^{59}$Co, and
$^{113}$In at the 10\% level. Neutrino-induced reactions contribute to a
similar extent to the production of radioactive ${}^{26}$Al and increase the
yield of $^{22}$Na by 50\%. Future $\gamma$~ray astronomy missions may reach
the precision at which the contribution from the $\nu$~process becomes
relevant. We find that the production of $^{22}$Na by the $\nu$~process could
explain the Ne-E(L) component of meteoritic graphite grains. The $\nu$~process
enhances the yield of $^{36}$Cl and we point out that the resulting
$^{36}$Cl/$^{35}$Cl ratio is in agreement with the values infrerred for the
early solar system. Our extended set of neutrino-nucleus interactions also
allows us to exclude any further effects of the $\nu$ process on stable nuclei
and to quantify the effects on numerous, hitherto unconsidered radioactive
nuclei, e.g., $^{36}$Cl, $^{72}$As, $^{84}$Rb, and $^{88}$Y.
