Nafion is one of the most common materials used for polyelectrolyte membranes and is the standard to which novel materials are compared. In spite of great interest in Nafion's nanostructure, it is still a subject of controversy. While multiple research efforts have addressed Nafion's morphology with Transmission Electron Microscopy, the results of these efforts have often been inconsistent and cannot satisfactorily describe the membrane structure. One of the reasons for differences in the reported results is the lack of sufficient control over the damage caused by electron beam irradiation. In this work, we describe some aspects of damage in the material that have a strong influence on the results. We show that irradiation causes mass loss and phase separation in the material and that the morphologies that have been observed are, in many cases, artifacts caused by damage. We study the effect of the sample temperature on damage and show that, while working at low temperature does not prevent damage and mass loss, it slows formation of damage-induced artifacts to the point where informative low-dose images of almost undamaged material may be collected. We find that charging of the sample has a substantial effect on the damage, and the importance of charge neutralization under irradiation is also seen by the large reduction of beam induced movement with the use of an objective aperture or a conductive support film. To help interpret the low-dose images, we can apply slightly higher exposures to etch away the hydrophobic phase with the electron beam and reveal the network formed by the hydrophilic phase. Energy loss spectroscopy shows evidence that fluorine removal governs the beam damage process.