Nafion, the polymer of choice in proton exchange membrane (PEM) fuel cells, contains complex networks of conductive channels that permit ion flow and enable these fuel cells to function. A complete understanding of the ion conduction process has not been realized, and a better understanding would lead to the production of more efficient PEM fuel cells. Ion movement in these channels produces electrical noise that we collect and analyze. Various statistical methods can be employed to investigate dynamically correlated regions inside these channels and can lead to a better understanding of the underlying dynamics of ion transport. Electrostatic force microscopy (EFM) techniques are employed here to probe dielectric noise in a protonated Nafion sample. We analyze fourth-order statistical fluctuations in order to determine spatio-temporal correlation lengths and their temperature dependence. The first harmonic response of an applied AC voltage between the conducting EFM tip and the conducting substrate beneath the thin film polymer sample is proportional to the sample’s local electric polarization. Noise in this signal is examined and many hours are recorded at various temperatures in order to improve statistical precision. We employ a variety of statistical analysis techniques ranging from power spectrum analysis to variance of autocorrelation functions in order to find deviations from Gaussian statistics. Super-sharp carbon nanotube EFM tips (nominal radius of 10 nm) are employed to probe smaller effective volumes and thus more easily detect these fluctuations. A connection is drawn between the dynamics found and those of glassy systems.