Yes, nuclear accidents increase mutation rate and with it the occurrence of various forms of cancer, but it seems those mutations aren't passed on to next generations (layman's explanation: if it doesn't kill you, it's unlikely to have an effect on your children. If it _does_ kill you, you aren't likely to have children) http://www.rerf.jp/radefx/genetics_e/birthdef.html:
"No statistically significant increase in major birth defects or other untoward pregnancy outcomes was seen among children of survivors. Monitoring of nearly all pregnancies in Hiroshima and Nagasaki began in 1948 and continued for six years.
[...]
In addition, a clinical health study of about 12,000 individuals was conducted between 2002 and 2006 with a focus on lifestyle diseases, based on the idea that adulthood is when disorders from radiation effects may develop. In this study, possible relationships between parental exposure and a combination of six multifactorial diseases (e.g., diabetes and hypertension) were analyzed, taking into consideration such lifestyle habits as drinking and smoking. The results showed no evidence at this time of increased risk of these multifactorial diseases among the target individuals. However, given that the subjects were still young at the time of the health examinations, with an average age of 48.6, it would be desirable to continue the clinical health study of this fixed cohort."
"WHETHER THE ATOMIC BOMBS dropped on Hiroshima and Nagasaki will have detectable genetic effects on the Japanese is a question of widespread interest. The purpose of the present note is to show briefly that (1) many difficulties beset any attempt to obtain a valid answer to this question and (2) even after a long-term study, such as that outlined below, it still may not be possible to determine just how much genetic damage was done at Hiroshima and Nagasaki."
"No statistically significant increase in major birth defects or other untoward pregnancy outcomes was seen among children of survivors. Monitoring of nearly all pregnancies in Hiroshima and Nagasaki began in 1948 and continued for six years. [...] In addition, a clinical health study of about 12,000 individuals was conducted between 2002 and 2006 with a focus on lifestyle diseases, based on the idea that adulthood is when disorders from radiation effects may develop. In this study, possible relationships between parental exposure and a combination of six multifactorial diseases (e.g., diabetes and hypertension) were analyzed, taking into consideration such lifestyle habits as drinking and smoking. The results showed no evidence at this time of increased risk of these multifactorial diseases among the target individuals. However, given that the subjects were still young at the time of the health examinations, with an average age of 48.6, it would be desirable to continue the clinical health study of this fixed cohort."
However, https://www.nap.edu/read/1800/chapter/3:
"WHETHER THE ATOMIC BOMBS dropped on Hiroshima and Nagasaki will have detectable genetic effects on the Japanese is a question of widespread interest. The purpose of the present note is to show briefly that (1) many difficulties beset any attempt to obtain a valid answer to this question and (2) even after a long-term study, such as that outlined below, it still may not be possible to determine just how much genetic damage was done at Hiroshima and Nagasaki."