We report results from an experimental study of coarsening in thin layers of succinonitrile in the presence of impurities. By quenching the latter from the liquid phase to different temperatures within the liquid-solid coexistence region, different solid area fractions φ are obtained. As φ is incresed from 0.13 to 0.40, liquidlike order develops among the coarsening crystals due to diffusional interactions. The latter give rise to local correlations between the size and rate of growth of crystals within a neighborhood of size ξ(φ). We study these and compare our findings with recent theoretical models of coarsening.