Genetic storage is way more resistant to bit rot than conventional computers. DNA is not stable, has a full time support system fixing it, and still has a relatively high mutation rate. But biological systems on the whole are much more resistant to individual errors.
Yes, single mutations can cause horrible diseases, but these mutations are either in the active site of proteins, or disrupt folding. A large portion of proteins are "bulk." If you look at protein simulations, only a small section of the protein is simulated, and the rest is just approximated as charged mass. Changes there are much less impactful and noticeable. As for it to be a disease, it had to be present at time of concept. If it happens during life (which is does, millions of times a day), the cell either ignores it or dies.