Error correction is immaterial for the factoring case. You multiply the factors and if you do not get the original number you know you have to run it again.
In Schor's algorithm, the quantum computer finds the period p of B mod N were N is the number you are trying to factor and B is a random number less than N. The quantum computer may find p with imperfect accuracy. Running the algorithm repeatedly can improve the accuracy of p. You can also try other numbers close to p. Both are examples of error correcting a quantum algorithm.
