Harris tells Liam emphatically "that is an ORDER from the United States Government".... only on TV would this happen. The government has processes for taking over a factory if needed, appropriating property if needed, but has no authority to compel a citizen to carry out orders. Furthermore the Undersecretary of Defense has no authority to present himself as "the United States government".
When the lieutenant is reporting about the details of the uranium transfer to Harris, he salutes, as he exits. While the Deputy Sec. Of Defense outranks him, he wouldn't salute a civilian other than the President. Additionally, the man was inside, and uncovered. (Not wearing a hat)
At 32:56, Jillian sees the sky and Mars. Mars is still very much at the same place it was when Liam had shown her that earlier, some 50 or more days have since passed. Planets don't stand still on the sky, they are called planet as it comes from the Greek planetai, meaning "wanderers". Mars should have moved, and they should have updated the sky picture accordingly.
Grace says about the Russian hotel room "This place probably hasn't been renovated since Lenin slept here." She had said in jest or satire, but what she implied is the right way. No one renovates the place of a great event. It is a protocol that such places have to be kept and maintained the way they were at the time of event, no changes, let alone renovations.
At about 16 mins Grace Barrow tells her daughter Zoe about her new beau. Zoe asks if their dating is allowed at the White House. Grace responds: "No, which is why I've had to be indiscreet." No one caught completely opposite meaning.