  Given a metric space $\langle X,\rho \rangle$, consider its hyperspace of
closed sets $CL(X)$ with the Wijsman topology $\tau_{W(\rho)}$. It is known
that $\langle{CL(X),\tau_{W(\rho)}}\rangle$ is metrizable if and only if $X$ is
separable and it is an open question by Di Maio and Meccariello whether this is
equivalent to $\langle{CL(X),\tau_{W(\rho)}}\rangle$ being normal. In this
paper we prove that if the weight of $X$ is a regular uncountable cardinal and
$X$ is locally separable, then $\langle{CL(X),\tau_{W(\rho)}}\rangle$ is not
normal. We also solve some questions by Cao, Junnilla and Moors regarding
isolated points in Wijsman hyperspaces.
