  We have investigated the peculiar structure of charge and spin ordering in
the half-doped layered perovskite oxide La$_{1.5}$Sr$_{0.5}$CoO$_4$ by elastic
neutron scattering. Two samples with different preparation histories were
studied. We find that the generic features of the ordered states, such as their
short-range, glassy nature and the spin incommensurability, are
sample-independent. At the same time, some subtle features of the ordered
phases, such as the correlation lengths, differ.
