  Second- and third-order results are presented for the structure functions of
charged-current deep-inelastic scattering in the framework of massless
perturbative QCD. We write down the two-loop differences between the
corresponding crossing-even and -odd coefficient functions, including those for
the longitudinal structure function not covered in the literature so far. At
three loops we compute the lowest five moments of these differences for all
three structure functions and provide approximate expressions in Bjorken-$x$
space. Also calculated is the related third-order coefficient-function
correction to the Gottfried sum rule. We confirm the conjectured suppression of
these quantities if the number of colours is large. Finally we derive the
second- and third-order QCD contributions to the Paschos-Wolfenstein ratio used
for the determination of the weak mixing angle from neutrino-nucleon
deep-inelastic scattering. These contributions are found to be small.
