Self renewal, differentiation assays, Flow cytometry for specific markers, in vivo differentiation assays,... There are good reviews about that subject. Good luck
To the points Benjamin Fournier made I like to add the capability of MSCs to undergo adipogenic , osteogenic, and chondrogenic differentiation in vitro. In this respect very important are also the conditions to maintain the stemness of MSCs. Besides other comprehensive reviews, all aspects including experimental details are well covered by the following articles: K Bieback et al. 2004, 2013, Ketterl, Bieback et al. 2015, and Mattar, Bieback et al. 2015.
not sure, in fact, that MESENCHYMAL stem cells are really pluripotent. Their self-renewal is limited to several passages (depending on cell species). Try to analyse cell immunophenotype (CD90+, CD73+, CD105+, SSEA4, lack of lineage-positive markers like CD45, CD14, CD8... These markers should be positive through subsequent passages in vitro. Stem cells should be positive for active telomerase. Your mesenchymal cells are capable to differentiate to osteo-, chondro- and adipocytes and, if pluripotent, to distict types as astrocytes or neural cells. Good luck.