The B-29 shown as the Enola Gay taxiing before takeoff has, incorrectly, it's defensive armament of machine guns. The B-29 as the Enola Gay shown taking off and flying the rest of the mission correctly does not.
In the movie the character Matt Cochran (played by Tom Drake) has an accident in the laboratory on Tinian that eventually kills him from radiation poison, but he is credited with saving 40,000 lives because of his self-sacrifice of bare-handedly separating the radioactive materials. This incident did not happen on Tinian. Rather, it reflects a similar accident that killed Canadian scientist Louis Slotin at Los Alamos NM in May 1946.
A "Little Boy" type uranium bomb, the type used at Hiroshima is shown being loaded onto the tower for the first A bomb test. Actually, a "Fat Man" type bomb (utilizing plutonium) was used in this test, this type later being used in the bombing of Nagasaki. (A "Little Boy" type bomb is correctly shown being carried by the Enola Gay in the bombing of Hiroshima.)
The "Little Boy" bomb that was dropped on Hiroshima was not aerodynamically-shaped like the one in the movie. Instead, it was cylindrical with a rounded blunt end and a box-like fins. Additionally, it was not loaded in Enola Gay as depicted in the movie; actually, the bomb was placed in a pit and the plane was moved over it for uploading.
The original Trinity Site bomb (called "the gadget" by the scientists) detonated in New Mexico in July 1945 was not the sleek, traditional bomb shape shown in the movie. Actually, "the gadget" was spherical and covered externally with wires.