Bud says he was 11 the first time he went on a "tiger cruise" with his father aboard the USS Arleigh Burke. The Arleigh Burke was not commissioned by the Navy until July 4, 1991, this episode takes place in 1997 and from his rank Bud's age is very likely 24 at the youngest, in 1991 he would have been 18. Bud would have been 11 in 1984, at that point the Arleigh Burke hadn't even been built yet, she was still on the drawing board.
The ship in this episode is supposed to be an Oliver Hazard Perry-class guided missile frigate, but the exterior shots of the ship go between that of a Perry-class frigate and an Arleigh Burke-class guided missile destroyer.
Not necessarily an error. Throughout the 10-year series ships names have not matched up with the hull numbers With the exception of "Ghost Ship" when the actual Hornet was shown and corresponded to her hull number 12. Usually the USS Seahawk CVN 65 was actually the USS Enterprise, while some shots of her flight deck were of the Stennis and the Kennedy. The name changes were obviously done on purpose, not in error.
Admiral Chegwidden says that the Stockdale carries a compliment of four Harpoon anti-ship missiles. The Stockdale is a Perry-class guided missile frigate, whose main armament is a Mk-13 missile launcher with a 40 missile magazine. Typically for most missions a Perry-class is armed with 20 SM-1MR anti-aircraft missiles and 20 Harpoon anti-ship missiles.
The ball caps indicate hull number FFG-62 (Guided Missile Frigate). There is no FFG-62. The highest number FFG is 61.
The base-caps of the crew aboard the "USS Stockdale" bear the designator FFG-62, while the hull bears the designator FFG-19 (USS John A. Moore). Both are visible on several occasions in this episode.