I liked the portrayal of Khrushchev in Space Race. He was by all accounts a pretty sane guy with a crude sense of humor ("Sputnik! We pulled the Americans' pants around their ankles!")
I once sent an email question to Sergey Khrushchev, Nikita's son. He immediately replied with his phone number, "Let's talk!". A very nice man.
Space Race was fun, I wouldn't suggest not seeing it. Just take all the interpersonal scenes with a grain of salt. For example, Korolev only spent a short time in a Gulag. He and Glushko were both under house arrest during the war, but working on Rocket projects for the government. They make it appear that Glushko was free and Korolev was digging trenches in Siberia the whole time. And Glushko would never have suggested Korolev to the authorities, as a rocket leader. When asked who they needed, he would have said "Me me me! Pick me!". In fact, both Korolev and Glushko owe their lives to Tupolov, the famous aircraft designer. He is the one who convinced Stalin that the two rocket scientists were too valuable to be shot or sent to Siberia. Almost every scene is a mistake of that order.