Hyper-Rayleigh scattering, HRS, is a powerful technique to extract the second-order polarizability, beta, of organic chromophores. However, we shaw that the obtained beta value, first, may differ depending on which of the three possible HRS data evaluation techniques is used and, second, may not agree with that determined by more conventional measurement techniques, such as electric field induced second harmonic generation, EFISH. The first problem is identified as being one essentially due to curve fitting when using the internal reference method, with the normalized internal reference method proposed as an alternative. The second problem has been identified as arising from a broad-band background signal which may contribute to the scattered intensity in the HRS measurement, underscoring the need to examine both the spectral purity of the scattered radiation and the dependence of the scattered intensity on fundamental intensity. This broad-band background has been examined in three molecules, where there was (i) either a negligible or a dominant contribution to the detected HRS intensity and (ii) either a quadratic or a cubic dependence on fundamental intensity. For two molecules, the broad-band background is identified as a three-photon-absorption induced fluorescence whereas the background signal for the third molecule displayed a quadratic dependence on fundamental intensity. The possibilities to circumvent the fluorescence problem via HRS measurements at longer fundamental wavelengths is discussed. Additionally, we also examine the case where the fundamental intensity is above the threshold for solution dielectric breakdown and/or higher-order contributions to the scattering intensity, and look at the effect this has on the extracted beta value.