Methods are presented for aligning the pivot point of a precessing electron probe in the scanning transmission electron microscope (STEM) and for assessing the spatial resolution in scanning precession electron diffraction (SPED) experiments. The alignment procedure is performed entirely in diffraction mode, minimising probe wander within the bright-field (BF) convergent beam electron diffraction (CBED) disk and is used to obtain high spatial resolution SPED maps. Through analysis of the power spectra of virtual bright-field images extracted from the SPED data, the precession-induced blur was measured as a function of precession angle. At low precession angles, SPED spatial resolution was limited by electronic noise in the scan coils; whereas at high precession angles SPED spatial resolution was limited by tilt-induced two-fold astigmatism caused by the positive spherical aberration of the probe-forming lens.