  We report on a calculation of the `mixed' strong and (purely) weak
corrections through the order $\alpha_{\mathrm{S}}^2\alpha_{\mathrm{W}}$ to
parton-parton processes in all possible channels at hadron colliders entering
the single jet inclusive cross section. At both Tevatron and LHC, such effects
are always negligible (below permille level) in the total integrated cross
section whilst they become sizable in differential rates. Specifically, if such
corrections are defined with respect to the full leading-order result of ${\cal
O}(\alpha_{\mathrm{S}}^2
+\alpha_{\mathrm{S}}\alpha_{\mathrm{EW}}+\alpha_{\mathrm{EW}}^2)$, we find
that, at the FNAL accelerator, they can reach the -5% benchmark in the jet
transverse energy (at the kinematical limit of the machine, rendering their
detection quite difficult). At the CERN collider, in the same observable, they
exceed the -10% level already at 1 TeV and can reach -40% at 4 TeV, kinematic
regions where such corrections will be comfortably observable for standard
luminosity. In addition, such corrections are somewhat sensitive to the
factorisation/renormalisation scale choice.
