The scientific community relies upon the veracity of the scientific data in handbooks and databases. In a previous work, the authors developed a systematic, intelligent, and potentially automatic method to detect errors in such resources based on artificial neural networks (ANNs). This method revealed variations from (10 to 900) % in tables of property data for elements in the periodic table and pointed out the ones that are most probably correct. In this paper, we focus on the details of employing this method for analyzing the data of boiling points and enthalpies of vaporization recorded in different handbooks. The method points out the values that are likely to be correct. To verify the method employed, a detailed discussion of the data with reference to the original literature sources is given as well as factors that may affect the accuracy of the prediction.