Factual error: Two rocket lift-offs are shown. For the American lift-off, they show an Atlas-Agena (American) rocket booster but for the Soviet lift-off, they show a Gemini-Titan (also American) rocket booster. Compounding the mixup is that the film's Jupiter capsules are basically just Gemini craft, which are seen atop what the film presents as the Russian rocket.
Factual error: Barbara takes an ancient document out of a filing cabinet. One of the words in its title is HIFTORIE, for "history." The old-fashioned way of writing the letter "s" was the so-called long s (ſ), not the letter "f", and this was only ever used as a lowercase letter. So the word would have been written as HISTORIE.