Before Mac interviews the FDO about a man overboard, a fly over shows a helicopter carrier, the next scene on board it's a jet carrier.
When Admiral Landry first sees Harm his shoulder boards have four stars. Later Sturgis referred to him as a three star.
When the bridge receives the word about the man overboard on the starboard side, the commanding officer, a four-stripe captain, orders, "Left full rudder, port engine stop!", then he orders the helmsman to "execute a Williamson turn". He orders exactly the opposite of what he should - that is, he should order, "Right full rudder, starboard engine stop" - to move the rudder so as to start the stern swinging away from the man overboard on the starboard side and to stop the starboard shaft to help with the turn and to reduce the probability of chewing up the victim with the starboard screw. Further, he should not order the helmsman to execute a Williamson turn - but rather he should turn over the conn back to the OOD, so that the OOD can give the required orders to the helmsman to make the Williamson turn. [A Williamson turn is a maneuver used to reverse the course of a ship and to return to the locus of the victim so as to search for and recover the victim.]
The Master Chief states the T-34C was found on its back, then further states the only damage was a bent strut and prop. If it had indeed flipped on its back, it would have canopy and vertical stabilizer damage as well, and would not be ready to fly the next morning. Besides, a metal prop strike requires an engine teardown for a bent crankshaft and other damage.