In a previous recent paper we discussed the limitations of the Fourier-based model in the prediction of visible moiré effects. Here, we extend the discussion to other mathematical models that are also being used in the moiré theory: the classical indicial equations method for modelling the moiré fringes between periodic or curvilinear gratings, and two methods that are used to model different facets of the moiré effects between correlated aperiodic layers. We discuss the limitations of each model, explain their significance, and suggest possible ways to overcome them.