Molecular Dynamics simulations are used to examine several key aspects of recent ultrafast infrared experiments on liquid water dynamics in an amplified and extended version of a recent communication [J. Phys. Chem. A 20027 106, 11993]. It is found that the relation between the OH stretch frequency and the length of the hydrogen bond in which the OH is involved is characterized by considerable dispersion. This dispersion, which is in part related to the varying OHO angle of the hydrogen bond, precludes a one-to-one correspondence between the OH frequency and the hydrogen bond length. Further, it is found that the time scale currently interpreted in terms of a stochastic modulation by the surrounding solvent of a highly frictionally damped hydrogen bond system is largely governed by hydrogen bond-breaking and -making dynamics, while the motion of an intact hydrogen-bonded complex is underdamped in character. A detailed analysis of these issues is provided for calculated spectral dynamics after creation of a hole in the ground vibrational state, in terms of a three time analysis (in addition to the H-bond period). Further, the validity of describing the OH frequency fluctuations as a Gaussian random process is examined, as is the character of the associated autocorrelation function of the OH frequency shift.