  The causal set approach to quantum gravity models spacetime as a discrete
structure - a causal set. Recent research has led to causal set models for the
retarded propagator for the Klein-Gordon equation and the d'Alembertian
operator. These models can be compared to their continuum counterparts via a
sprinkling process. It has been shown that the models agree exactly with the
continuum quantities in the limit of an infinite sprinkling density - the
continuum limit. This paper obtains the correction terms for these models for
sprinkled causal sets with a finite sprinkling density. These correction terms
are an important step towards testable differences between the continuum and
discrete models that could provide evidence of spacetime discreteness.
