When I saw it at the theater I didn't know what was coming until I saw the B-29 (Bock's Car) make its final turn on its bomb run. My jaw dropped. I couldn't remember a single movie that contained scenes of the A-bombings of Japan. Having said that, 3 thoughts occurred regarding the accuracy ...
1. I would have thought the B-29 would have been flying at a higher altitude.
2. I got the impression from the Wolverine film that the Fat Man detonated at ground level. I thought it was set for an air burst at ~1,000 ft.
3. There were other B-29s in the Bock's Car flight. I would have thought they would have been close by.
A final note - I toured the USAF Museum at WP-AFB in 1994. The fuselage flight deck of Bock's Car was on display then while the rest was being restored.
I thought that the flash should have been a lot brighter. Instead all the damaage seemed to come from the shock wave. But that may be just the higher yield H-bombs. And I think I recall it being an air burst as well because of Nagasaki’s hilly terrain.
As a matter of fact I recall reading about Hiroshima victims who were instantly blinded by looking directly at the explosion, so I suppose the flash should have been brighter in the movie.