Since its development, the scanning transmission electron microscope has rapidly found uses right across the material sciences. Its use of a finely focussed electron probe rastered across samples offers the microscopist a variety of imaging and spectroscopy signals in parallel. These signals are individually intuitive to interpret, and collectively immensely powerful as a research tool. Unsurprisingly then, much attention is concentrated on the optical quality of the electron probes used. The introduction of multi-pole hardware to correct optical distortions has yielded a step-change in imaging performance; now with spherical and other remnant aberrations greatly reduced, larger probe forming apertures are suddenly available. Probes formed by such apertures exhibit a much improved and routinely sub-Angstrom diffraction-limited resolution, as well as a greatly increased probe current for spectroscopic work. The superb fineness of the electron beams and enormous magnifications now achievable make the STEM instrument one of the most sensitive scientific instruments developed by man, and this thesis will deal with two core issues that suddenly become important in this new aberration-corrected era. With this new found sensitivity comes the risk of imaging-distortion from outside influences such as acoustic or mechanical vibrations. These can corrupt the data in an unsatisfactory manner and counter the natural interpretability of the technique. Methods to identify and diagnose this distortion will be discussed, and a new technique developed to restore the corrupted data presented. Secondly, the subtleties of probe-shape in the multi-pole corrected STEM are extensively evaluated via simulation, with the contrast-transfer capabilities across defocus explored in detail. From this investigation a new technique of STEM focal-series reconstruction (FSR) is developed to compensate for the small remnant aberrations that still persist – recovering the sample object function free from any optical distortion. In both cases the methodologies were developed into automated computer codes and example restorations from the two techniques are shown (separately, although in principal the scan-corrected output is compatible with FSR). The performance of these results has been quantified with respect to several factors including; image resolution, signal-noise ratio, sample-drift, low frequency instability, and quantitative image intensity. The techniques developed are offered as practical tools for the microscopist wishing to push the performance of their instrument just that little bit further.