When they are swearing Gary Nance as president, they refer to him as the 45th president of the United States. This means that Mitchell would be the 44th. George W. Bush is the 43rd President of the United States. Barack Obama is the 44th President of the United States.
United States Senator 'Alfonse D'Amato' was set to cameo as himself but then pulled out of the film following issues between the Senate and Warner Brothers over the content in Ice-T's album "Cop Killer". D'Amato later attempted to return to the film after Ice-T parted ways with Warner Brothers but director Ivan Reitman turned him down.
When Dave is taken from the Capitol to the hospital he is taken to the Bethesda Naval Center in Bethesda, MD (based on the visual of that facility). This clearly is not the closest trauma hospital to the Capitol and would not be where the President would have been taken.