Consider the noise model for which bit and phase errors occur independently on each spin, both with probability p. When p is low, this will create sparsely distributed pairs of anyons which have not moved far from their point of creation. Correction can be achieved by identifying the pairs that the anyons were created in (up to an equivalence class), and then re-annihilating them to remove the errors. As p increases, however, it becomes more ambiguous as to how the anyons may be paired without risking the formation of topologically non-trivial loops. This gives a threshold probability, under which the error correction will almost certainly succeed. Through a mapping to the random-bond Ising model, this critical probability has been found to be around 11%.