President Kirkman makes two mistakes regarding military rank when helping to serve food in the mess line. First, he calls a Specialist 4 a Corporal. Then, he calls the next person in line a Private when they are also a Specialist 4.
When the President is serving the soldiers bacon, he calls the female soldier a Corporal and the male soldier a Private, when they are both seen wearing the rank of a Specialist. Also the female soldier says that she is on her second tour of duty, and has spent a total of 4 years there. Army combat tours are usually 12 months.
Emily tells Seth that he is facing a felony possession charge because modafinil is a schedule III controlled substance. It is in fact a schedule IV controlled substance, but he would still be facing a felony charge for having such a large quantity.
Command elements in Afghanistan don't generally work out of tents. Certainly not the level of command the President would be involved at. Everything shown that takes place in Afghanistan would have been in a normal building. The types of tents shown wouldn't be used for more than a few months, let alone after we've been in the same spot for 17 years. The wind alone in central Afghanistan would quickly destroy them.
When the president first enters the military tent at the beginning of the episode, one of the American flags behind him with only 48 stars.
In the end, the cake the president gets is not the same as the one on the plane.
When Seth is speaking with the journalist back in his office, the clock on the wall shows the same time for POTUS as it does for Washington DC. Washington is 8.5 hours behind Kabul, Afghanistan, so if the President is in the Kabul time zone and it's 17:25 in Washington DC, the clock should be reading 01:55.
President Kirkman's visit to Afghanistan is supposed to be top secret, yet Air Force One is parked for more than a day on the airbase's tarmac without any camouflage and within plain sight of anyone who happens to walk by, two of whom are the leaders that the president is meeting, including the head of a terrorist cell. The press would have been made aware of Air Force One's location almost immediately.
While discussing his arrest with Emily, Seth says that he managed to conceal the fact that he works for Kirkman from the arresting officer. As the White House's liaison to the media, Seth has a high degree of visibility; it would extremely difficult to keep his place of employment a secret in the time between his booking and arraignment and when Kendra bails him out the following day.