The well-known significant systematic disagreements between cross sections of partial photoneutron reactions (γ,1n) and (γ, 2n) obtained in various experiments majority of which have been carried out at Livermore (USA) and Saclay (France) were analyzed using the objective physical criteria of data reliability. It was found that experimental data for more than 50 nuclei from 51V to 209Bi in general do not meet those criteria and therefore are more or less unreliable. The experimental-theoretical method based on the Combined PhotoNuclear Reaction Model (CPNRM) was used to evaluate partial reaction cross sections that meet the reliability criteria. It was shown using the analysis in detail of differences between evaluated and experimental cross sections that the major sources of large systematic uncertainties in obtained cross sections are certain shortcomings of experimental neutron multiplicity sorting method have been used for indirect separation of partial reactions. It was shown that the newly evaluated cross sections of partial photoneutron reactions differ significantly (at least noticeably) from the ones obtained using the method of neutron multiplicity sorting but agree with experimental data obtained by alternative methods used for reliable direct separation of partial reactions. The consolidated review of many problems with partial photoneutron reaction experimental data reliability and some ways to solve ones are presented.