Well I remember my dad telling me once that when he was a kid, his mother would tell them not to eat the snow after they did nuclear testing in nevada because the fallout would make the rain and the snow radioactive, now my dad was a kid in the 60's so it's about this time period, and my grandmothers thinking is/was on par with the general 50's idea and 30's idea too. also my grandmother is still alive today.. thats neither here nor there, anyway yeah my point is radiation can travel far and cause mutations, even if the area wasn't even directly hit, my dad and grandparents lived and grew up in maine by the way.
Well, radiation can't really cause many mutations. Minor ones, but not Fallout style ones. I mean, at the most, you'd get birth defects or something. Also, I think the fallout from those Nevada tests would've settled within the general vicinity of Neveda.