  The ${\cal O}(\alpha)$ radiative corrections to the process
$p\,p\hskip-7pt\hbox{$^{^{(\!-\!)}}$} \rightarrow \gamma^*, \, Z \rightarrow
\ell^+ \ell^-$ ($\ell=e,\,\mu$) are calculated. Factorizing the collinear
singularity associated with initial state photon bremsstrahlung into the parton
distribution functions, we find that initial state corrections have a much
smaller effect than final state radiative corrections. Due to mass singular
logarithmic terms associated with photons emitted collinear with one of the
final state leptons, QED radiative corrections strongly affect the shape of the
di-lepton invariant mass distribution, the lepton transverse momentum spectrum,
and the forward backward asymmetry, $A_{FB}$. They lead to a sizeable shift in
the $Z$ boson mass extracted from data, decrease the di-lepton cross section by
up to 10\%, and increase the integrated forward backward asymmetry in the $Z$
peak region by about 7\% at the Tevatron. We also investigate how experimental
lepton identification requirements modify the effect of the QED corrections,
and study the prospects for a high precision measurement of
$\sin^2\theta^{lept}_{eff}$ using the forward backward asymmetry at the Large
Hadron Collider (LHC).
