Ionic liquids (ILs) show a variety of unusual and intriguing properties on a molecular level. Recently, a new type of structural anomaly occurring in neat ILs near their glass transition temperatures (T-g) has been found. In particular, the coexistence of two types of IL environments was observed, one of which progressively suppresses the molecular mobility upon temperature increase within similar to(T-g-60 K) and T-g. To clarify the nature of these anomalies, their general characteristics, and potential for applications, in this work we investigated the molecular mobility in binary mixtures of IL [Bmim]BF4 with water using electron paramagnetic resonance spectroscopy and spin probes (stable nitroxides TEMPO-D-18, (2,2,6,6-tetramethylpiperidin-1-yl)oxyl, and 14-carbamoyl-7-azadispiro[5.1.5.2]pentadeca-14-ene-7-oxyl). In a series of such mixtures with water content X-H2O = 0.2-50 wt %, we detected similar anomalies to those found in neat IL (x(H2O) = 0). For x(H2O) < 2.5 wt %, the differences in manifestations of structural anomalies are negligible compared to those in neat ILs. In the range 2.5 <= X-H2O < 5 wt %, an abrupt partial suppression of anomaly is observed, but further increase of the water content up to X-H2O = 50 wt % has no impact on anomaly since, most plausibly, it leads only to the growth of the water-rich domains. Consequently, the observed structural anomalies are rather robust against the presence of water in ILs, which is beneficial for their potential applications.