In another online venue, I was asked this question recently: Could radiation damage bring about random mutation of nanobots?
The answer I gave was: Yes and no.
Yes, radiation damage will occur. Is that a problem? Yes, it's a problem for the individual nanobot or nanosystem that is damaged or disabled. However, current designs for molecular manufacturing do not include free-roaming nanites; that has been shown to be less efficient than a model in which all the nanobots are fastened down inside a nanofactory.
It has also been shown that vast amounts of redundancy can be built in at very low cost, making radiation damage essentially irrelevant, at least during the working life of each nanofactory (which likely will be made obselete by a more advanced model within months).
As for random mutation, remember that each case of radiation damage is far more likely to be disadvantageous rather than advantageous. So, right from the start, the odds are stacked against progression via mutation.
The other important point is that evolutionary mutation only applies in cases of reproduction, as in biology with the passing on of instructions for assembly via DNA. But with the nanofactory concept, individual nanobots will not reproduce -- indeed, they will carry no instructions for replication; it will literally be impossible.
You can get a good sense of how this all fits together by watching a recently produced short film on productive nanosystems.