How accurate does polar alignment need to be?

It depends entirely on what comes next. Visual observing tolerates a rough aim at Polaris; a two-minute exposure at long focal length needs the reticle routine; guided imaging needs better still.

There is no single answer, and quoting one would be pretending the question has no context.

For visual observing

Aiming the polar axis roughly at Polaris keeps an object in a medium-power field for a long time. The remaining drift is slow enough to ignore, and a nudge on the slow-motion control resets it.

For short exposures on a tracker

The polar scope reticle routine, or a phone application that shows where the pole sits. This is the level at which exposures of a minute or two behind a wide lens stay clean.

For long exposures at long focal length

Better than a reticle can easily achieve by eye, which is why software routines that measure the error directly exist. At this point the alignment is a measurement rather than an aim.

The test that settles it

Expose for the length you actually want, and look at the corners. Everything trailing in one direction is alignment; everything trailing in different directions at the edges is optics; stars round in the middle and trailed at the very edge is field rotation, which says the alignment is off in a particular way.

If this page and the manufacturer’s own documentation disagree, follow the documentation. Every aperture, focal length, payload rating, field, eye relief, transmission figure and thread size on this page comes from the maker’s own published figures, with the unit as printed and the source named. None of it is measured here, and no figure is converted into another convention, because a converted number is a different number. And for any payload figure: makers quote it for observing, and photography asks for a considerably wider margin. A tracking error invisible at the eyepiece is a smeared star on a sensor, and the rating usually excludes the counterweights. This page reports the maker’s figure with the use it was quoted for, and derives no photographic capacity from it.