The use of the Local critique plot is illustrated by three different applications. The applications involve directed acyclic graph (DAG) models of varying complexity and structure, and they illustrate different aspects and abilities of the plots. We see examples where the posterior is a trade off of tail specifications because of conflict between the local prior and the lifted likelihood. Hence model choices made on these tails are, perhaps unexpectedly, identified as influential. We also see how the local critique plot can reveal local prior or lifted likelihood domination. The applications also illustrate that diagnostic warnings from the local critique plot prompt us to reconsider the statistical model, but that sometimes a reexamination can assure us that the choices are justified.