At the fundraising party, Donna says she sees Matthew Perry, and heads off to talk to him. This will later cause a continuity issue with the West Wing universe, as in seasons 4 and 5 of the show, Matthew Perry plays recurring character Joe Quincy.
A shot of the wing of Air Force One show a winglet found on the 747-400. Air Force One was built on a different model which doesn't have winglets.
The President's plane is said to land at around 6am, with him leaving LAX at 6:20am. The shot of the plane taxiing into the airport is in bright sunlight. In Los Angeles, in January and February, the sun rises at around 7:00am. The plane would have arrived in relative darkness.
When Joey Lucas speaks with Josh about flag burning, she quotes an old proverb in Latin "Vox populi, vox Dei". Her sign language translator pronounce the "i" in "populi" as in Iowa when it must be pronounced as in Indiana.
At around the 18:23 mark, when Josh, Toby, and Sam are turning to walk inside, you hear Josh as "How is he doing in there?". His mouth isn't moving. You then hear Sam's response, but it's off by just tiny amount. It also doesn't match the background noise of the rest of the shot. Both of these lines were dubbed in after the fact.
In the background of the scene in which the Motorcade is arriving at Andrews AFB the tail of a Canadian Airlines 737 can be seen. Andrews does not have passenger traffic.
When the President's motorcade is first shown (when the President is arriving at LAX and traveling to the hotel), the motorcade is shown turning south onto Sepulveda Boulevard from Manchester Boulevard in Westchester, past the distinctive Loyola Theatre (now a medical building). This would take them towards LAX, not away from it. (The motorcade vehicles arrive ahead of Air Force One in Air Force cargo planes, typically the C-17, and would have be staged at the airport for his arrival.)
C.J. is approached by a studio representative offering her a "development deal." She makes a big point of not understanding what that is, both with him and then later with Sam. As revealed in later episodes, before working on the President's election campaign, C.J. worked as a publicist in Los Angeles. Although she indicated she was not suited to being an entertainment publicist, she should have been familiar with what development was.