  Radiative corrections in pole approximation, which are based on the leading
contribution in a systematic expansion of amplitudes about resonance poles,
naturally decompose into factorizable corrections attributed to the production
or decay of the resonance and non-factorizable corrections induced by soft
photon (or gluon) exchange between those subprocesses. In this paper we
complete an earlier calculation of mixed QCD$\times$electroweak corrections of
$\mathcal{O}(\alpha_s\alpha)$ to the neutral-current Drell-Yan cross section in
pole approximation by including the previously neglected corrections that are
solely related to the Z-boson production process. We present numerical results
both for differential distributions and for the forward-backward asymmetry
differential in the lepton-pair invariant mass, which is the key observable in
the measurement of the effective weak mixing angle at the LHC. Carefully
disentangling the various types of factorizable and non-factorizable
corrections, we find (as expected in our earlier work) that the by far most
important contribution at $\mathcal{O}(\alpha_s\alpha)$ originates from the
interplay of initial-state QCD corrections and electroweak final-state
corrections.
