When Leo and Adm. Fitzwallace are sitting in the Situation Room discussing what to do about Qumari Defense Minister Shareef, Fitzwallace states, "I've been a soldier for thirty-eight years." The problem with this statement is that Fitz is a Naval Officer - a distinction in service branch that is apparently overlooked by the scriptwriters: a member of the Navy would actually refer to himself/herself as a sailor, not a soldier. In American military jargon, 'soldier' denotes one who serves in the Army.
Leo says that the US government spent millions of dollars developing a pen that could be used in space while the Russians simply used a pencil. The US also used a pencil. The Fisher Space Pen was developed privately with no funds from the US government.
US Navy Admiral Percy "Fitz" Fitzwallace (John Amos), Chairman of the Joint Chiefs of Staff, at one point refers to himself as a "soldier". A member of the US Navy would never say this. They would instead say "sailor" or "officer", or more specifically they would say their rank (ie: "Master Chief", or "Lieutenant Commander") or their occupation (ie: "naval aviator" or "special warfare operator"). "Soldier" is specific to the US Army only and not the Navy, Marine Corps, Air Force or Coast Guard.
When President Bartlet is leaving the cemetery at the beginning of the episode, the window in the limo is down. It is clearly a standard issue window, even though the President's limousine has bulletproof windows, which are anywhere from 2 to 5 inches (508-1270 mm) thick. Also, the President would not ride with the window open.
When C.J. fires the first shot from Donovan's revolver, she is wearing ear protection, but Donovan isn't. When he fires the other five shots into the target, neither are wearing ear protection. The report of a .357 Magnum in an enclosed space like the pistol range would be deafening without hearing protection. Neither of them would be able to make themselves heard without shouting. Further, neither puts on eye protection, although another shooter in the range is wearing it. Eye and ear protection is usually required when entering an indoor pistol range.
When Donovan puts away his revolver, he sticks it in his waistband and flinches because the barrel is still hot. An on-duty Secret Service special agent, especially one so well-acquainted with firearms as Donovan is, would carry the revolver in an approved holster, not stuck in his waistband.