Previous proposals for the origin of molecular homochirality, based on the effect of the weak neutral current (W-NC) on enantiomers, and the amplification of the resultant parity-violating energy difference (PVED), are possibly flawed. The additive amplification of PVED in crystals and polymers ("Yamagata hypothesis") cannot lead to detectable levels of optical activity, the original theory apparently overestimating PVED by a factor equal to Avogadro's number. An alternative theory based on the irreversible and spontaneous evolution of a dynamically fluctuating system is apparently impractical. However, the nonlinear amplification of PVED via autocatalytic polymerization may be possible as indicated by a simplified physico-chemical approach. This may also occur during crystallization and melting, and form the basis of the second order asymmetric transformation. (Thus, reported differences in the melting points of enantiomers in several cases may well be real). Also, the preponderance of racemic compounds over conglomerates may be based on the destabilization of the conglomerate by the action of the WNC on the crystalline lattice. The WNC may also be involved in the anomalous scattering of X-rays, which possibly arises from their circular polarization: the current theory would need to be revised accordingly.