The reverse Monte Carlo method in its molecular version, is used to analyze neutron diffraction data for water in two thermodynamic states around its critical point. At the lower density we find that the oxygen-oxygen and the oxygen-hydrogen partial radial distribution functions cannot be reproduced simultaneously in a satisfactory way. At the higher density the first peak of the oxygen-hydrogen partial radial distribution function, which gives a measure of the number of hydrogen bonded neighbors, turns out to be unreproducible. To understand the possible origin of these discrepancies the reverse Monte Carlo method is applied to the analysis of the radial distribution functions which are obtained directly by Fourier transforming the measured structure factors. This procedure reveals that at the lower density the total radial distribution function measured in light water can be responsible for the apparent deviations between simulated and experimental curves. At the higher density the experimental inaccuracy in the measurements of both light and half-deuterated water structure factors is found to affect the evaluation of the partial radial distribution functions. The results of the present work demonstrate that reverse Monte Carlo is a valuable method for revealing experimental inaccuracies, and therefore its use in the data reduction process is suggested.