When arriving onboard the Seahawk, Harm is not wearing any warfare insignia on his dress whites. Though he's now a JAG, as a former pilot he would still be entitled to wear his Naval Aviator insignia. The insignia is only revoked if the aviator's flight status is revoked for cause at an evaluation board. As Harm lost his flight status due to a medical issue, this would not be the case.
When Rabb and Pike arrive aboard the carrier, they are greeted by Ens. Roberts. Although uncovered, Roberts salutes the senior officers. The Navy and Marines do not salute while uncovered. At most, they will momentarily snap to attention.
In the closing shot, Rabb and Pike are pressed back into their seats as the COD is launched off the carrier. The seats in the COD are rear facing to protect the occupants during carrier landings. They should have been thrown forward into their harnesses.
During the ATARS flight, CAG is wounded and Harm flies the plane back to the carrier and lands. No F-14 had dual controls. The rear-seater, RIO, if his pilot is wounded and unable to fly the aircraft, can only eject both of them and hope the pilot survives the ejection and landing.
When Rabb and Pike enter Crypto, Rabb gets a badge authorizing him to be in the room; Pike already has hers. When they leave, they walk out wearing their Crypto badges. That is a breach of security protocol. Such badges are never to be visible outside of a secure room where they can be photographed and copied.
When Admiral Brovo learns of Lt. Arutti's disappearance, he wonders if JAG can dump the case onto NIS. NIS had become NCIS in 1992, three years before JAG (1995) premiered.
In the pilot episode when Harm is talking to the ZNN reporter, he sets a tub of ice cream on the table. The tablecloth visibly moves, however, there is no sound.