Mesenchymal stem cells (MSC) exhibit enormous heterogeneity which can modify their regenerative properties and therefore influence therapeutic effectiveness as well as safety of these cells transplantation. In addition the high phenotypic plasticity of MSC population makes it enormously sensitive to any changes in environmental properties including fluctuation in oxygen concentration. We have shown here that lowering oxygen level far below air atmosphere has a beneficial impact on various parameters characteristic for umbilical cord Wharton Jelly- (WJ-) MSC and adipose tissue- (AD-) derived MSC cultures. This includes their cellular composition, rate of proliferation, and maintenance of stemness properties together with commitment to cell differentiation toward mesodermal and neural lineages. In addition, the culture genomic stability increased significantly during long-term cell passaging and eventually protected cells against spontaneous transformation. Also by comparing of two routinely used methods of MSCs isolation (mechanical versus enzymatic) we have found substantial divergence arising between cell culture properties increasing along the time of cultivation in vitro. Thus, in this paper we highlight the urgent necessity to develop the more sensitive and selective methods for prediction and control cells fate and functioning during the time of growth in vitro.