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If you look at the Wikipedia page List of nearest stars and brown dwarfs , you'll notice that all stars mentioned in the list have a very precise value; all are $\pm0.02$ ly (except for GJ 1005, but it is still within 1 ly)

Even though WISE J0521+1025 is within 5 parsecs of Earth, its uncertainty is 1.3 parsecs (4.3 ly)! What is going on here, and why is the distance so inaccurate?

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The distance is that reported by Bihain et al. (2013), which is based on a mean relationship between absolute magnitude and spectral type that has a lot of scatter.

i.e. in contrast to most (all?) the other objects in that list, there is no reported trigonometric parallax measurement for this very faint T7.5 brown dwarf.

In fact, if it turned out to be a binary brown dwarf, the distance could be incorrect!

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