Modern sextants can read the angle to a 0.1 minute level of accuracy, i.e. one-600th of a degree or one-tenth of a mile. In practice, actual accuracy to one-half mile is acceptable and quite good. The usual standard is accuracy to within five miles. The sextant (or octant) is meant to get the ship across the ocean. Once near the coast (20-100 miles) the more accurate techniques of piloting are relied upon for a safe landfall. The sextant is still the standard instrument for taking the observations required for celestial navigation.

https://www.ion.org/Museum/item_view.cfm?cid=2&scid=14&iid=2...

One thing that helps with a pitching deck is that the horizon and object remain the same angle. Like a camera following race car, the objects move together.