Continuity: When Donna is writing on a pad to Josh when awaiting surgery, she first writes "Nice hat!!!" A few seconds later we see the pad again, and the exclamation marks have disappeared. Shortly after, they are back.

Deliberate "mistake": While a nice approximation, the helicopter used as 'Marine One' is significantly different (and much smaller) than the real ones used by the real White House (http://www.minihelicopter.net/Marine1/MarineOne.jpg).

Continuity: Leo enters the situation room and is told the "planes are on the deck". He watches a video feed as a plane is launched from the USS Lincoln. The S3-B Viking is seen approaching one camera (single vertical tail fin, wing-mounted engines), then from another angle, we see an F-14 Tomcat lifting off (dual tails and fuselage-mounted engines) and moving away from camera. This is supposed to be live video, and it isn't possible two different jets are launching from the same carrier at the same exact moment, so it can only be a bad choice of stock footage by the show's makers.