When Annie comes into the JAG office, she does not have a visitor's badge.
When Josh climbs into the F14 you can see a crewman along the wall in the hanger trying to get out of the shot.
When Harm, Mac, and the admiral board the ship in search of the kidnapped boy, the admiral is shown holding his pistol with his finger on the trigger (inside the trigger guard), something a trained SEAL should never do.