  The form factors for the semileptonic decays of heavy-light pseudoscalar
mesons of the type $D \to Ke\nu$ are studied in quenched lattice QCD at
$\beta=6.0$ using Wilson fermions. We explore new numerical techniques for
improving the signal and study $O(a)$ corrections using three different lattice
transcriptions of the vector current. We present a detailed discussion of the
relation of these lattice currents to the continuum vector current and show
that the disagreement between the previous results is to a large extent due to
the value of $Z_V$ used in the calculations. We also present results for the
decay constants of light-light, heavy-light and heavy-heavy mesons.
