What is an important limitation of SEMs and TEMs in observing organisms?

Answer 1

Zoom scale. SEMs and TEMs are both meant to observe extremely small objects (in the case of TEMs, image resolution is on the order of 50 picometers or half an Angstrom, according to Wikipedia - Angstrom is the unit used when discussing the diameter of atoms in crystalline structures, to give you an idea of scale). Nothing biological is anywhere near that small. They could be used to examine DNA strands or similarly small bits of an organism, but there is no way to fit even the smallest bacterium into the image so you can examine how it functions as a whole - a critical aspect of Biology. Even a virus might be tough to fit into the image field, though I could be wrong there - viruses are absurdly tiny.

Another possible limitation (though I can't be sure about this) is the possibility that electron microscopes won't be able to pierce the cellular membrane. Standard backlit optical microscopes use light that filters through the membranes to distinguish features within, often with a still-living cell, enabling study of the cell functions in real-time. I'm unsure as to whether or not the electron beam used by electron microscopes would behave similarly to visible light - predicting electron behavior is where physics starts to get wonky, even when you know Quantum mechanics, which I don't.