The Marine sentries at the White House are missing their covers (i.e. hats), which they should be wearing when on duty at their posts.
At Barksdale AFB the Air Force officers are wearing their hats indoors; they're typically removed when the wearer is inside.
The Navy sailors at the Pentagon breakfast and at Camp David are wearing the "Salt-and-Pepper" uniform (black pants with white shirt) that was discontinued in the 1980s.
A young Navy sailor at the Pentagon is wearing a United Nations Korea Medal ribbon on his shirt, which is from the 1950s.
USAF officer McGrath on Air Force One wears a United Nations Korea Medal on his uniform jacket, which is from the 1950s.
One of the Army soldiers at Barksdale AFB is armed with an M16A1 rifle; by 2001 that rifle had been replaced by the M16A2.
Washington, D.C. police (MPDC) are seen on the Pentagon grounds immediately after it is attacked by the hijacked plane; the Pentagon is in Arlington County, Virginia so the Arlington County Police (ACPD) would have been there instead immediately after the plane crash.
When on the phone with Rice, Bush says "DEFCON Delta" when he should have said "THREATCON Delta". Later on in the film, Rice makes the same mistake as well, saying "DEFCON Delta" instead of "THREATCON Delta".
Bush and several others mispronounce "PEOC"; it's pronounced as one word rather than as individual letters.