It is probably a good idea to do some extra QC filtering (such as for cells with a minimum number of covered genes, and cells with a sufficiently low percentage of mitochondrial reads), but the criteria that can/should be applied will likely vary between projects.
I'm not sure how easy it is to do this with Monocle (or what specific functions to recommend). However, some other potential options would be:
1) Use direct counts for p-values (and use relatively standard RNA-Seq methods like edgeR / limma-voom, or you may be able to try some scRNA-Seq specific methods like MAST), and use CPM values for calculating fold-changes (or some other normalized count, if the goal is to have something to compare to what is provided by the differential expression program)
2) Use Seurat scaled expression for the fold-change calculation, and potentially use standard statistical tests (like
lm() for linear-regression,
aov() for ANOVA, etc.) to compare differential expression between groups of cells.