  Precision studies of the production of a high-transverse momentum lepton in
association with missing energy at hadron colliders require that electroweak
and QCD higher-order contributions are simultaneously taken into account in
theoretical predictions and data analysis. Here we present a detailed
phenomenological study of the impact of electroweak and strong contributions,
as well as of their combination, to all the observables relevant for the
various facets of the $p\smartpap \to {\rm lepton} + X$ physics programme at
hadron colliders, including luminosity monitoring and Parton Distribution
Functions constraint, $W$ precision physics and search for new physics signals.
We provide a theoretical recipe to carefully combine electroweak and strong
corrections, that are mandatory in view of the challenging experimental
accuracy already reached at the Fermilab Tevatron and aimed at the CERN LHC,
and discuss the uncertainty inherent the combination. We conclude that the
theoretical accuracy of our calculation can be conservatively estimated to be
about 2% for standard event selections at the Tevatron and the LHC, and about
5% in the very high $W$ transverse mass/lepton transverse momentum tails. We
also provide arguments for a more aggressive error estimate (about 1% and 3%,
respectively) and conclude that in order to attain a one per cent accuracy: 1)
exact mixed ${\cal O}(\alpha \alpha_s)$ corrections should be computed in
addition to the already available NNLO QCD contributions and two-loop
electroweak Sudakov logarithms; 2) QCD and electroweak corrections should be
coherently included into a single event generator.
