The samples themselves are plunge frozen into vitreous ice using liquid ethane, so they won't move much on their own. The electron beam, as well as the stage they sit on inside the microscope do cause movement of the grid/sample, however, and so on modern microscopes, what we actually record are movies so that we can correct for things like beam induced motion with software.

Exposure is a separate variable because it also causes sample degradation. Ideally, a microscope is only shooting one electron at a time at the sample (that never happens obviously), but the fewer electrons, the better. On overexposed micrographs, you can see the burn marks on the sample.