As a rule, the modern theories of nucleation represent only modifications of classical theory, and they still remain unsuitable for quantitative prediction of experimental results. In order to create the universal description of supersaturated vapor nucleation, as well as evaluate other theories, we need to get the reliable experimental results. Now experimental skills are high enough for precision measurements of the vapor nucleation rates as well as for detecting and evaluating, for example, temperatures of phase transitions in the new phase critical embryos. That is, one can find experimentally the singularity of the nucleation rate surface at conditions for the critical embryo phase transitions. Visual analysis of the experimental results has the low potential to detect the nucleation rate surface singularity and the surface singularity can be missed sometimes. One major problem for singularity detection is the noise of experimental results. This problem still exists even if one has experimental results of high accuracy. The condition for surface continuity and monotony could be applied as a criterion for analysis of experimental data for the vapor nucleation rates. The criterion is tested for the broad spectrum of the experimental results in the vapor nucleation. As an example of the criterion being used, the experimental results for the n-pentanol-water binary system of nucleation have been analyzed. A peculiarity of this system is the existence of a miscibility gap between the components. It was found that the criterion as a function of n-pentanol mole fraction has the singularity in the vicinity of this gap. This singularity was smoothed in the experimental results presentation and omitted in the original research. The proposed criterion can be used to search the experimental data set singularity as a function of their variable(s).