If you're worried about bad pixels or noise, it seems like there is an easy fix: point it in a direction specified by some angles theta & phi, wait long enough to accumulate light from distant faint objects (high redshift galaxies etc), then shift Webb's orientation by a small amount to theta+delta_1 & phi+delta_2, which will have a significant overlap with the original image, and after taking the 2nd image check to make sure that all the objects have shifted over together by the same amount...