When the President calls the Secret Service agent in the hospital near the end, in one shot the agent has a breathing tube in his nose. The shot cuts to the President, and then in the next shot the breathing tube is gone.
Five minutes before the end, When Kirkman gets on a call with Ritter, Ritter is shown with a Nasal Cannula, But later in the conversation Ritter is shown without it.
The shooter strafes the governor's dinner with what is clearly an automatic weapon. In the aftermath it is stated that the shooter used an AR15. The AR15 is not an automatic weapon and has no automatic setting. It is a semi automatic only weapon which can not be fired at the rate down in the dinner shooting, and is very difficult to be turned into an automatic weapon, requiring high end milling equipment and very high end gunsmith knowledge. This is a common mistake in Hollywood.
Protocol requires honors for a Head of State to be 4 Ruffles and Flourishes and the national anthem for that country. It has been the custom when the US President attends a less ceremonial gathering (like the Governor's Dinner in this episode), he will still receive the 4 Ruffles and Flourishes, but "Hail To The Chief" is substituted for the National Anthem. This allows the President and his party to move to where they will be seated, and also greet friends and officials along the way without everyone standing at attention. At the Governor's Dinner, only 1 Ruffle and Flourish was played and "Hail To The Chief" was severely abbreviated, likely for pacing reasons.
At the Governors' meeting, it's stated several times that all 50 Governers are present, however, there is only enough seating for the 36 shown.