Other mistake: When Jenny Lind is on stage singing 'Never Enough' during her American debut, she is in a very large theater with a crowded audience, and full orchestra. Obviously she would have to be miced, and have her voice amplified, for such a large space. When she is actually singing, her character's voice (or rather the dubbed voice of Loren Allred) is greatly amplified, with sound effects. But during this actual scene, there is no microphone or amplification system present. She does not have a microphone stand in front of her. There is no microphone hanging from the ceiling, or anywhere on stage that we can see. Technology was limited at that time, so she would not be using any type of cordless headset, or wireless microphone, which cannot be seen anyway. Her character's voice is obviously amplified a great deal through a microphone, which doesn't seem to exist.
Other mistake: The designer asking Khrushchev about what type of curtains they should have for the funeral. He first says "ruched" for the sample in his right hand and "not ruched" for the left. He then continues, but instead says "not ruched" for the right hand sample and "ruched" for the left. (00:59:30)