When Toby and Sam are meeting with Congressman Kimball regarding sustaining the veto, one of the terms he demands is a GAO (Government Accountability Office) audit regarding application of a farm bill. GAO is an arm of Congress, not the Executive Branch, so it would be unnecessary (and possibly counterproductive) for Kimball to seek the White House's help For such an audit.
During the briefing in the Situation Room, Leo McGarry is informed that 12 Israeli F-15s are preparing to take-off each armed with eight "AIM Sidewinders". The correct designation for this missile is the "AIM-9 Sidewinder" and while the F-15 is capable of carrying a total of eight air-to-air missiles, it can carry no more than a maximum of four AIM-9 Sidewinders at any given time. Also, why exactly these aircraft would be armed only with short-range air-to-air missiles in what is described to be a ground attack mission is peculiar, especially since the Palestinians do not possess an air force.
A military advisor refers to AH-64 Apache attack helicopters as "Douglas AH Apache Longbows". The correct designation is the "AH-64D Apache Longbow". The "AH" simply indicates that it is an attack helicopter but does not signify the type. F-22 fighters are never referred to as Lockheed-Martin "F" Raptors and the Apache would never be simply called an "AH".
Furthermore, Douglas Aircraft Company merged with McDonnell Aircraft in 1967 (creating McDonnell Douglas) long before the Apache helicopter even existed. So referring to the manufacturer as Douglas is a significant misnomer. The Apache was originally produced by Hughes, then by McDonnell Douglas, and is currently built by Boeing (and had been for several years before this episode aired). So at the time it would have been correctly identified as a Boeing AH-64D Apache Longbow. And while McDonnell Douglas would probably still be acceptable, it's doubtful a military expert would ever refer to the Apache as having been made by Douglas.
The president's veto is referenced as his first in office. In In This White House (2000), the president is referenced to have vetoed the Republicans' education bill the year before.
When Toby Ziegler asks Josh Lyman what the day before Yom Kippur is called, Josh pronounces Erev as e-REV, when the emphasis is actually placed on the first syllable. In addition, it is unlikely that even non-observant Jews would not be aware that the day before the most important holy day in the Jewish calendar is called Erev Yom Kippur. While Josh has never been seen in a Jewish context, it had already been established that Toby goes to synagogue on Saturday morning. In all probability he is a Conservative Jew. A Conservative Jew would know that the day before Yom Kippur is called Erev Yom Kippur.