I believe that genetics have a relatively minor impact on our mental ability. Our DNA species wide is SO DAMN similar that I don't think that it can have that big of an impact. It does have some impact, but there are SO many other factors contributing to it:
Health and diet of the pregnant mother
Diet as a youth
Current diet
Safe and mostly stress free childhood
Good education and educators
Cultural and family attitude towards education
Presence of mentally stimulating activities as a youth
Presence of peers and frequent opportunities to socialize
I think all those things have as much of an impact on one's mental abilities as genetics. Yes, the savants and geniuses are going to have an exceptional set of genetics going in, even to have a chance, but they are the exception, as most people are closer to average.
Can "inferior" DNA (1) make a person more likely to commit crime?
DNA by definition, doesn't make any decisions for any human, the exception being someone with a genetic disorder who isn't capable of adult thought. Thought is something completely separate from the purposes of DNA. Crime or lawlessness is a learned behavior based on their own decision making process.
(1) if there is such a thing as "inferior DNA". I think there's an argument here to be made about the subjective quality of inferior and superior---if anyone would like to take up that avenue, please do
Like zip said, Inferior DNA is only ever defined by whether it is successful in surviving it's current environment. The weaker, slower, dumber, sicker, or diseased are eliminated by natural selection. But natural selection isn't always flawless, except when it comes to the inability to reproduce.
Africans have only been genetically separated from the rest of us for a blink of the evolutionary eye. If we are any genetically different, we're talking extremely minor differences. That brings us to what, if any, evidence there is to support Watson's supposed statements. Those pieces of evidence would have to be individually examined for validity.