Plot hole: When Captain Towers gives his XO an injection to allow him to die in peace, he, properly, swabs the site with alcohol, and slips the needle into the vein. However, immediately below the injection site, is a hep-lock.a port installed into a vein to allow injectables to be administered. I cannot imagine that a senior Naval officer would be so ignorant of the port's function.
Factual error: Capt. Towers (4 rings on his shoulder) would be addressed as Captain, not Commander. And when he was promoted to Admiral he never displayed that rank.
Visible crew/equipment: When Yeoman Swain views his hometown through a periscope, you see someone walking along the waterfront. Suddenly this person takes a dive behind a barrier, realizing there's not supposed to be anyone alive. (02:12:00 - 02:13:00)