During the flight to Hiroshima, the footage alternates between a B-29 and a B-17. The B-17 engines are staggered on the wing from the fuselage, while the B-29 engines are straight on the wing.
A recording was being listened to of Dr. Leo Szilard in Chicago at Los Alamos by General Groves. The wide plastic reels are reel-to-reel audio. Tape recordings were a product of BASF and other wartime German developers but tapes and did not exist prior to the technology being brought here as captured alien property in 1946. Prior to this in the United States, technology was so far behind, recordings were made on wire or the usual acetate disk.
The London double-decker bus seen at the beginning, supposedly in 1933, is a Routemaster, a type not introduced until 1954.
The footage of the first atomic explosion, the "Trinity" test, shows various archival footage of atomic blasts that occurred in the ocean. In one shot you can see the waves lapping the shore.
Near the first of the film, where General Groves is observing some of the chemistry and physics put on the blackboard by Dr. Vincent (played by Fritz Buchinger), an error is shown with Vincent making several entries, two to be culminating: ten to the 23rd power, only supposedly Vincent makes an error and shows in the second equation put up in rapid succession, "10 to the 24th." This was done seemingly by the filmmakers so General Groves could then point out that he had been following the mathematics and as a show of his prowess, he announces that he did not see "How in the second equation the formula shows ten to the 24th." This then permits his speech about having ten years of postgraduate education which he believes is equivalent to two PhD's. The mathematical equation Dr. Vincent is citing is the factor of Avogadro's Law relating to the mass of a gas which is 6.023 X 10 to the 23rd. This is a factor taught in Chemistry 101.