Contrary to conventional wisdom, the transmission and detection of signals, efficiency of kinetics in the presence of fluctuating barriers or system's synchronization to the applied driving may be enhanced by random noise. We have numerically analyzed effects of the addition of external noise to a dynamical system representing a bistable over-damped oscillator and detected constructive influence of noise in the phenomena of resonant activation (RA), stochastic resonance (SR), dynamical hysteresis and noise-induced stability (NES). We have documented that all above- mentioned effects can be observed in the very same system, although for slightly different regimes of parameters characterizing external periodic driving or (and) noise. Particular emphasis has been given to presentation of various quantifiers of the noise-induced constructive phenomena and their sensitivity to the location and character of the imposed boundary condition.