When Carter tells O'Neill that Washington D.C. is her "old stomping grounds", Jack replies, "Sorry to hear that." When Selig is playing back the recording of the conversation for Jack in the bar, his reply became "My condolences."
As Sha're/Amonhet approaches Apophis after having given birth, her large belly is still visible. While this may seem like an error, it is important to note that at most it has been a couple hours since giving birth and while her belly would be somewhat deflated now that she is no longer carrying a child, it would still be fairly large. While Amonhet would be able to heal her from the pains and stress of natural childbirth, the Goa'uld do not possess the ability to instantly return a body to its peek physical condition. Sha're's body would still show the signs of recent weight gain and childbirth, including a larger stomach.
While Jack O'Neill sits on the bench talking to Selig, the inside end of the epaulet on his right shoulder is out from under and on top of his lapel, which it should not be. This is so for multiple shots. When he stands from the bench, it is still out. But after he walks up the steps and turns back to talk to Selig (delivering his famous "other Col. O'Neil" lines), the epaulet is no longer out of place.
Although the Air Medal is an honor and a distinguished award, it is awarded for duty while in aerial flight and it is nowhere close enough in order of precedence to have the recipients flown to D.C. and awarded by the President. Up until this episode, both O'Neill and Carter could easily be up for the AF Cross or Defense Distinguished Service Medal. The minimum award might be the Distinguished Flying Cross. "The Air Medal is awarded to any person who, while serving in any capacity in or with the armed forces of the United States, shall have distinguished himself by meritorious achievement while participating in aerial flight. Awards may be made to recognize single acts of merit or heroism or for meritorious service."
However, the award was explicitly given for "destroying two Goa'uld spacecraft which were poised to attach Earth." The metals were given for doing so while aboard those ships which were in orbit around Earth at the time.
When Teal'c warns of the incoming activation of the gate while pretending to be one of Heru'ur's guards, he uses the term "Stargate". This term is used only by SGC; the Goa'uld and Jaffa call it "Chappa'ai".
Jack repeatedly walks around outdoors in Washington DC in full uniform without his "cover" (his hat). No officer would do so, doubly so in DC.