Corrected entry: When Cooper and the Prime Minister are watching the Sky News report, it is night time outside, but the time on the live report reads 15:48. The news is being broadcast in Britain and Sky News is a British news channel so there would be no time difference.
Continuity mistake: When playing Donkey Kong in the competition, Cooper finishes Level 22 by jumping over the last piece holding the Ape up and then it says "GAME OVER," when he should go to the next level.
Correction: While the airing of the news is live, they are not watching it live. It was recorded so they could watch it later with the president (such as on a DVR). They even pause it at the end.
Bishop73