We study the temporal growth pattern of surface fluctuations on a series of spinodally unstable polymer films where the instability can be adjusted with the film thickness, h(0). For the most unstable film studied (whose vertical bar(h(0) - h(sp))/h(sp)vertical bar = 0.988; h(sp) is the thickness where the second derivative of the interfacial potential of the film equals zero), the growth rate function of the Surface modes as a function of the wavevector fits well to the mean-field theory. When the film thickness is increased such that vertical bar(h(0) - h(sp))/h(sp)vertical bar <= 0.977. the mean-field theory demonstrates marked disagreement with experiment, notwithstanding the provision of the known corrections from nonlinear effects and thermal noise. We show that the deviations arise from large-amplitude fluctuations induced by homogeneous nucleation. which are not considered in the conventional treatments.