HSP have been criticized for lacking the formal theoretical derivation of Hildebrand solubility parameters. All practical correlations of phase equilibrium involve certain assumptions that may or may not apply to a given system. In particular, all solubility parameter-based theories have a fundamental limitation that they apply only to associated solutions (i.e., they can only predict positive deviations from Raoults law): they cannot account for negative deviations from Raoults law that result from effects such as solvation (often important in water-soluble polymers) or the formation of electron donor acceptor complexes.  Like any simple predictive theory, HSP are best used for screening with data used to validate the predictions. Hansen parameters have been used to estimate Flory-Huggins Chi parameters, often with reasonable accuracy.
The factor of 4 in front of the dispersion term in the calculation of Ra has been the subject of debate. There is some theoretical basis for the factor of four (see Ch 2 of Ref 1 and also. However, there are clearly systems (e.g. Bottino et al., "Solubility parameters of poly(vinylidene fluoride)" J. Polym. Sci. Part B: Polymer Physics 26(4), 785-79, 1988) where the regions of solubility are far more eccentric than predicted by the standard Hansen theory.
HSP effects can be over-ridden by size effects (small molecules such as methanol can give "anomalous results").
It has been shown that it is possible to calculate HSP via molecular dynamics techniques, though currently the polar and hydrogen bonding parameters cannot reliably be partitioned in a manner that is compatible with Hansen's values.