1) Cold field emission guns. The big challenge of an electron source is producing a coherent beam - that is a beam that comes off the tip one electron at a time, at the same location, the same angle, and with the same energy. The cooler the tip runs, the more coherent it tends to be. This has made a big difference and is just now widely commercially available.

2) Narrow pole-piece gap. The sample on most TEMs sits sandwiched between two objective lenses that operate in tandem - these are typically called twin objectives. The upper one ensures the beam is parallel, which primarily results in uniform defocus (or focus if one so desires) across the image. The lower one is responsible for image formation and initial magnification (actually, all of your resolution essentially). The gap between them is responsible for your primary aberrations: spherical and chromatic. Reducing this gap reduces the total aberrations in the image.

I will side bar that the physics of a microscope are not really holding it back from what I'm doing - generating structures of biomolecules. Really, I'm more limited by the camera technology than anything, because the cameras simply aren't performant enough to dose the images to the level I'd like, to collect as many images as possible in as short a time as possible. Fundamentally, I tend to be limited by number of observations.

For the really cutting edge stuff...check out ptychography:

https://en.wikipedia.org/wiki/Ptychography

>How does one become a microscopist as a profession? It seems like a specialized field with a narrow entry point and a lot of hoops.

There are basically two routes for TEM - material science, or biochemistry. The way to become a microscopist for me was to show up at a University that had a grant for a microscope, but no one to operate it. :)

In general, universities operate TEM cores, frequently called bioimaging or something. (Structural biology if it's newer although that's just one application among many). Frequently there are positions for all education levels - bachelor's through PhD, depending on what one wants to do. Training is a mix of hands on (interfacing with complicated systems) and theoretical (physics and image formation). Typically the operators aren't the most theoretical, but have a lot of very niche practical knowledge you only get from being around broken microscopes.