At the magnetic poles, the magnetic compass does not point south or north, it points down! At the magnetic poles, the direction of the magnetic flux is perpendicular to the surface of the earth. However, as the magnetic poles and the geographic poles are not in the same place, this is only a problem at the magnetic poles.
When navigating in polar regions, astronomical methods work well, and a system called "Isogriv" mavigation can be used as well. Isogriv navigation relies on the angle of magmetic variation between the users posititon, the magnetic pole and the destination. Used by someone who is skilled in the method, it is quite accurate, but in inexperienced hands it is easy to make enormous errors.
Some years ago, an aircraft was shot down over Central Siberia following a trans-polar flight which supposed to be going to Tokyo. The enquiry concluded that the navigator, who had never used the Isogriv system before, had made an error of almost 90 degrees, and at the time of the interception was nearly 1200 miles off course.
Marine and aircraft compasses are designed to function over about 98% of the earth's surface, and only become inaccurate within a few miles of the magnetic poles.
Due to the influence of electro-magnetic phenomena in the upper atmosphere, GPS is unreliable in high latitudes, and ground-based radio navigation systems can also be badly affected. Rather than a conventional sextant, which requires a level horizon, the bubble sextant or the theodolite are used for astro navigation.
Modern navigation aids like gyro cmpasses and inertial navigation systems make polar navigation easier, and some radio navigation systems can be used, as long as the navigator is aware of, and takes account of,the limitations of the system in use.
I hope this information is helpful.
Alan.