For example, you could store the correct genetic code in digital form, using redundancy and error detection algorithms to preserve that data forever (well, until the heat death of the universe). Then, whenever you set up a cloning batch you take a sample to test against the digital copy. If there's any mutation, the batch is discarded. If there's no mutation, then the batch is considered "good" and you cook up more source stock from it.
There is, of course, a chance that some of the newly cloned cells have mutations. I'm assuming that the testing process is destructive and relatively expensive, so some mutated cells will make it through the screens. However, as long as the testing process is used, the mutation will not propogate beyond a generation.
This all assumes, of course, that the Rimmerworld civilization is so obsessed with "racial purity" that only perfect clones are acceptable.