The command ball caps that the crew of the USS Monroe wear all bear the SEAL Trident. This insignia would not be used for this. The correct insignia should be the Enlisted or Officer Surface Warfare insignia (as appropriate).
The old chief is wearing a Submarine Warfare insignia. While possible for someone to have served on both submarines and surface combatants, he should have an Enlisted Surface Warfare insignia placed above his pocket and the Submarine Warfare below that on the pocket flap.
PO Baker says he is going to resign. Petty Officers are enlisted and can't just resign. He would have to wait out his term of enlistment (4-6 years) before he could be discharged. He could request a transfer to another ship.
Navy Lieutenant Commanders wear gold oak leaf collar insignia, not silver ones.
At 18:45 Jarod encounters the man he found welding at 15:15, who states he is Lieutenant Albert Danes. He is grossly out of uniform- his jumpsuit bears the fouled anchors rank insignia of a Chief Petty Officer.