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 (Tg) 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 (Tg-60 K) and Tg. 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-D18, (2,2,6,6-tetramethylpiperidin-1-yl)oxyl, and 14-carbamoyl-7-azadispiro[126.96.36.199]pentadeca-14-ene-7-oxyl). In a series of such mixtures with water content xH2O = 0.2-50 wt %, we detected similar anomalies to those found in neat IL (xH2O = 0). For xH2O < 2.5 wt %, the differences in manifestations of structural anomalies are negligible compared to those in neat ILs. In the range 2.5 ≤ xH2O < 5 wt %, an abrupt partial suppression of anomaly is observed, but further increase of the water content up to xH2O = 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.