The standard theory of the dynamics of superfluid films, although in good qualitative agreement with experiment, is not in perfect quantitative agreement. Until now it has not been clear whether the disagreement is due to inaccuracies in the theory or because the experiments involve an extra physical effect not included in the theoretical model. Here we show how the theory can be refined: the ambiguity that arises over the difference between free and bound vortices in the superfluid system is avoided by using an ansatz in which all vortices are considered paired; the interaction between vortices is calculated using recently developed versions of the Kosterlitz recursion relations accurate to higher order in the fugacity; the linear response is calculated using accurate numerical techniques. We present a detailed comparison of the modified theory's predictions with recent experimental results. We find that, despite the changes in the theory, the agreement with experiment remains only qualitative, suggesting that the theory fails to capture some of the essential physics of experiments on Helium films.