  We study the consequences of disorder in the Kitaev honeycomb model,
considering both site dilution and exchange randomness. We show that a single
vacancy binds a flux and induces a local moment. This moment is polarised by an
applied field $h$: in the gapless phase, for small $h$ the local susceptibility
diverges as $\chi(h)\sim\ln(1/h)$; for a pair of nearby vacancies on the same
sublattice, this even increases to $\chi(h)\sim1/(h[\ln(1/h)]^{3/2})$. By
contrast, weak exchange randomness does not qualitatively alter the
susceptibility but has its signature in the heat capacity, which in the gapless
phase is power law in temperature with an exponent dependent on disorder
strength.
