So the Earth has a giant magnetic field we use to determine direction. The field roughly looks like a magnetic dipole, but because the field is generated by a turbulent liquid dynamo near the Earth's core, it's not a perfect dipole.
This leads me to believe that as you approach the magnetic north or south poles, your compass reading will become increasingly vague, and that there's probably a finite region near the pole where the compass direction rather randomly points some direction other than the pole itself.
Additionally, as you near the pole of a perfect dipole, the component of the magnetic field tangent to the surface approaches a magnitude of zero. Because real-world compasses have friction, imperfect magnets, and so forth, there's surely some minimum field strength required to accurately move the compass magnet.
Finally, I know that the pole has daily cycles as well as long-term movements. My guess is the daily cycles can be predicted with some kind of almanac or equation, and that travelers near the pole could receive periodic updates as to the center of the daily cycles so they could adjust their local declination accordingly. Still, there would be some kind of precision error here that might be significant.
Between the three effects above (and possibly others I don't know about), I'm guessing there's a real-world limit on how close you can get to the exact magnetic pole before a real-world compass can no longer be trusted.
How close can we get to the magnetic pole and still use a compass to determine direction?
To narrow the scope of the question, I'm thinking of a standard compass I can pick up at Walmart for like $10 (say, this one). However, answers regarding high-end compasses and very low-end compasses (like, a magnetized needle through a cork floating in water) would also be appreciated.
Additionally, my question relates to humans using compasses for navigation, so if the answer is less than a few hundred meters, that's close enough to "right on the pole" for my purposes. At that point, you could simply look at the building or other landmark you're trying to find. Conversely, if the answer is several hundred miles, that would make it impossible to use traditional compass-based navigation between settlements near the magnetic pole.