When Tommy Crickshaw and Hazel Huffman are discussing communism, the camera shot from behind Crickshaw shows his hand in a fist, cut to the next shot facing him, his hand is stretched out.
Diego Rivera's mural in Rockefeller Center was destroyed in February of 1934. The unauthorized performance of "The Cradle Will Rock" took place on 16 June 1937. Hallie Flanagan testified before Congressman Dies' committee on 6 December 1938. For artistic effect, the film makes it seem that the three events occur simultaneously.
Mistakenly depicts superstar Marion Davies as a public drunk and smoker. Davies did not smoke and she did her drinking at home.
The Diego Rivera mural, as depicted in the film, is not his original Rockefeller Center version design (for which in-progress photographs exist), but of the smaller re-creation Rivera did a year later in Palacio de Bellas Artes in Mexico City. The Rockefeller Center mural was larger, whereas the spatial arrangement of features in the re-creation (and in the film) is more compact.
At the beginning of Hallie Flanagan's Senate testimony, the court stenograper's machines are not operating although they are pressing the keys. Later in the scene, the machines are working properly.
During the discussion in the Federal Theatre Project office early in the film, a (color) wall map of the USA can be seen including Alaska and Hawaii. Neither of these states were part of the union in 1936, but were U.S. territories.
The opening scene takes place in "Fall 1936", but the newsreel says Italian forces are "poised to invade" Ethiopia. The invasion actually took place in October 1935.
When Italy invaded, Ethiopia was still known as Abyssinia
In the opening exterior NYC street sequence following Olive, just as John Turturro's credit is supered, a window mounted air conditioner is visible in the alleyway behind. While home air conditioning was introduced in 1928, it was extremely rare until after World War II, and it's not clear the design shown was available at the time.
At 36 when the film was released, Angus Macfadyen is visibly far older than Orson Welles was supposed to be during the time the film is set. When the opens, in 1935, he was only 20 years old and even at the climax, in 1937, he'd still only be 22.