  We prove a counting theorem concerning the number of lattice points for the
dual lattices of weakly admissible lattices in an inhomogeneously expanding
box, which generalises a counting theorem of Skriganov. The error term is
expressed in terms of a certain function $\nu(\Gamma^\perp,\cdot)$ of the dual
lattice $\Gamma^\perp$, and we carefully analyse the relation of this quantity
with $\nu(\Gamma,\cdot)$. In particular, we show that
$\nu(\Gamma^\perp,\cdot)=\nu(\Gamma,\cdot)$ for any unimodular lattice of rank
2, but that for higher ranks it is in general not possible to bound one
function in terms of the other. Finally, we apply our counting theorem to
establish asymptotics for the number of Diophantine approximations with bounded
denominator as the denominator bound gets large.
