It is shown that a strong but diffuse dielectric anomaly, commonly expected only in disordered ferroelectrics, may be inherent in strained and defect-free perovskite ferroelectric thin films. The origin of this unusual anomaly, which was never predicted for a defect-free system, is the overcritical trace of a critical point in the film phase diagram, This possibility is illustrated by the mean-field thermodynamic calculations performed for (111)-oriented PbTiO3 films epitaxially grown on dissimilar cubic substrates. It is shown that clear symmetry reasons exist for the unusual behavior of the system. The essential prediction of the theory is that the type of the dielectric anomaly can be tailored by the sign of the misfit strain imposed on the film in paraelectric state: compressive strain leads to a standard Curie-Weiss anomaly, whereas the tensile one results in a diffuse anomaly.