  In this paper we determine the weak-interaction corrections of order
$\alpha_s^2\alpha$ to hadronic top-quark pair production. First we compute the
one-loop weak corrections to $t \bar t$ production due to gluon fusion and the
order $\alpha_s^2\alpha$ corrections to $t \bar t$ production due to
(anti)quark gluon scattering in the Standard Model. With our previous result
this yields the complete corrections of order $\alpha_s^2\alpha$ to $gg$, $q
\bar q$, $q g$, and ${\bar q} g$ induced hadronic $t \bar t$ production with
$t$ and $\bar t$ polarizations and spin-correlations fully taken into account.
For the Tevatron and the LHC we determine the weak contributions to the
transverse top-momentum and to the $t \bar t$ invariant mass distributions. At
the LHC these corrections can be of the order of 10 percent compared with the
leading-order results, for large $p_T$ and $\mtt$, respectively. Apart from
parity-even $t \bar t$ spin correlations we analyze also parity-violating
double and single spin asymmetries, and show how they are related if CP
invariance holds. For $t$ (and $\bar t$) quarks which decay semileptonically,
we compute a resulting charged-lepton forward-backward asymmetry $A_{PV}$ with
respect to the $t$ ($\bar t$) direction, which is of the order of one percent
at the LHC for suitable invariant-mass cuts.
