Simon Donovan can be seen putting away the armed robber's gun. When he gets up, his own gun is not in his hand, and he didn't have enough time to put it away.
Toby decides to send President Bartlet's motorcade to tie up traffic in an effort to prevent Ritchie from getting to the theatre. A motorcade would never leave the President's location, in case something happened which required a quick evacuation of the President. Additionally, it is highly unlikely that the White House Communications Director could direct the movement of a Presidential motorcade.
Fitzwallace indicates that the defense minister will be returning home on a Gulfstream business jet. The plane that is shown landing is a Learjet 35, distinguishable by the wingtip fuel tanks.
There is reference to a disused RAF airfield in Bermuda. There is no disused RAF airfield other than the seaplane base which a Lear jet couldn't use even in an emergency.
CJ states that the president will be in his seat for the five and 1/2 hour hour performance of a theatrical performance in NYC at 7:30 PM, and President Bartlet would certainly not show up late for this show. A reporter questions her about the supposed early start time. 7:30 is actually a late start time as most evening performances start at 7:00. Due to being so long, the show would end after 1:00 AM if they started at 7:30.
When Josh and Amy are discussing welfare, they are doing so at a Tully's Coffee. Tully's Coffee only has stores in the western United States and none in Washington D.C.
When Simon calls in the robbery, he gives the location as being on Broadway in the upper 90's. This is a couple of miles from the theater and, even if he were going to the Secret Service field office (as CJ notes later), he'd be going the wrong way; the field office was moved to Brooklyn after the September 11 attacks.
When WH-COS Leo enters the room at the scene of the briefing of gang-of-8 on the assassination, the gang (8 congressmen) and J-COS Fitzwallace stand up . That kind of respect from an audience of that profile in WH is reserved solely for POTUS.