A "misaligned" corner borders three rather than four polygons. Although not all such corners will be misaligned--such things can happen around the perimeter of the PLSS system and along natural boundaries--finding these places will provide an efficient screen that picks up all misaligned corners with very few false positives.
It may be difficult to identify "corners," though. Instead I propose doing the calculation with a raster representation of the data: the focal variety in a 2 x 2 neighborhood will equal 3 at all potentially misaligned corners.
You need to use a cellsize small enough to detect slight misalignments. This limits the resolution to about 100 meters when processing the entire US, for otherwise the grid will become unmanageably large. A practical limit is around 10-25 meters, achieved by processing the regions in smaller tiles.
As a check of this approach I carried out the focal variety calculation in geographic coordinates on a 0.001 degree grid covering half the conterminous US. It contains a half billion cells representing nearly 40,000 PLSS polygons. (It occupies 84 MB on disk in its native ESRI format.)
This figure shows potentially misaligned corner cells in red and apparently aligned ones in cyan.
This trial calculation consumed less than 25 MB RAM and required one minute to complete. It found 26,225 cells with a focal variety of 3. Because each misalignment introduces two such cells, this suggests approximately (26000/2)/40000 = around one-third of all corners are "misaligned." This includes corners occurring along natural boundaries (rivers, creeks, and large lakes), etc.