Neither the book nor the film make direct reference to the Rosenberg events (though Lumet did claim that the execution scene was 'as it happened').
The introduction of Susan as the younger child (rather than the second son of the Rosenbergs), and her lingering death, appears to be an attempt to distance the novel from being considered biographical.
Other key differences include - Rochelle is a college graduate, Paul is not; this is the reverse of the Rosenbergs. Mindish appears to be a fusion of two historical figures, Morton Sobell and David Greenglass.
A key scene (in part 1), is the family's attendance at the Robeson concert at Peekskill (1949); in the novel Paul leaves the bus to argue with the right-wing protesters and is violently set upon by them.
Another key scene has Daniel taking part in the 1967 anti-Vietnam war march on the Pentagon.