I think mutation rate would be subject to evolution as well. We can evolve to do more, or less DNA repair (and checks; up to acute radiation poisoning, cell self destruct is good enough).
Also, the effects of radioactivity are presumed linear. Extrapolating from high doses, the doses of up to 10x our natural background must have extremely minor effect on the mutation rate, vast majority of mutations arising due to other causes.
(The radiation releases in nuclear accidents are only a big deal because very huge number of people is exposed, resulting in massive dis-utility even if cancer rate increase is very minor)
Not entirely relevant to the main issues of lesswrong, but possibly still of interest: my talk entitled "von Neumann probes and Dyson spheres: what exploratory engineering can tell us about the Fermi paradox".
Abstract: The Fermi paradox is the contrast between the high estimate of the likelihood of extraterritorial civilizations, and the lack of visible evidence of them. But what sort of evidence should we expect to see? This is what exploratory engineering can tell us, giving us estimates of what kind of cosmic structures are plausibly constructable by advanced civilizations, and what traces they would leave. Based on our current knowledge, it seems that it would be easy for such a civilization to rapidly occupy vast swathes of the universe in a visible fashion. There are game-theoretic reasons to suppose that they would do so. This leads to a worsening of the Fermi paradox, reducing the likelihood of "advanced but unseen" civilizations, even in other galaxies.
The slides from the talk can be found here (thanks, Luke!).