  We analyze the dynamics of the ion-dipole pairing reaction in the
two-dimensional Coulomb gas in the presence of disorder. Sufficiently singular
disorder forces the critical temperature of the Kosterlitz-Thouless-Berezinskii
fixed point to be non-universal. This disorder leads to anomalous ion pairing
kinetics with a continuously variable decay exponent. Sufficiently strong
disorder eliminates the transition altogether. For ions that are chemically
reactive, anomalous kinetics with a continuously variable decay exponent also
occurs in the high-temperature regime. The Coulomb interaction inhibits
reactant segregation, and so the ionic $A^+ +B^- \to \emptyset$ reaction
behaves like the nonionic $A + A \to \emptyset$ reaction.
