What if the
1961 Goldsboro B-52 Crash had the 2 nuclear bombs it was carrying detonate? How many would die?
Thousands easily. Perhaps hundreds of thousands from fallout and related problems.
How would US and world governments react?
The US would be humiliated on top of (partially) irradiated. The Soviets would have had a field day with the news. America's allies would look nervously at those missile bases and patrolling bombers. The image of the US being the competent leader of the free world would take a major hit.
How would it effect the Cuban missile crisis and the whole cold war?
In my opinion, hard to say. The US may be more cautious, and perhaps traumatized, by what happened. The allies host to US nukes, as I said above, may be even more wary of hosting such devices on their soil. The Soviets may be emboldened by such a display of bad luck as an act of incompetence, or they may quietly double check their own supply. I could see the Missile Crisis still occurring per OTL, however.
How would nuclear power be viewed today?
Even more skeptically and cynically than it is in our world. It may also be severely curtailed to non-existent in America.
And generally would super powers still have nuclear weapons today?
Absolutely. America will have several other "broken arrows," and will require nuclear weapons to achieve parity and deterrence with the Soviets. The Soviets will see nukes as the same means to challenge the West. A freak accident wiping part of North Carolina away will do little to change that.
EDIT: Also, could it have been mistaken for a Soviet nuclear attack and start WWIII?
Highly doubtful. We would have been able to piece together the trajectory and a missing plane, and any first Soviet strike would be much larger, against other targets, and coming from another direction.