When the film was made in 1952, no Flower Class corvettes remained in Royal Navy service. The ship used was therefore the Greek corvette Kriezis, ex-HMS Coreopsis. She was given the number K49 in the film which was the number of HMS Crocus (sometimes wrongly thought to have been used in the film). The real number of the Coreopsis was K32. She was brought back to Britain for scrapping. She had already been scrapped by the time the film premiered.
Two versions were shot of the scene where Captain Ericson talks to Lieutenant Lockhart about having to blow up his own men in the water. In one version he shed one tear, and in the second version he shed two tears. The second version was used.
Donald Sinden was originally supposed to play First Lieutenant James Bennett, until Stanley Baker was cast instead. Therefore Sinden ended up playing the much larger role of Sub-Lieuetenant (later Lieutenant-Commander) Keith Lockhart.
On boarding the castle class frigate, Ericson and Lockhart question whether there is actually a castle called 'Saltash Castle'. There is a castle in Saltash but it is more correctly called Trematon Castle.
If you look carefully, you will see that the rank insignia on Ericson's (Jack Hawkins') sleeves are in a different "font" from those of the other officers on his ship. This is because Ericson is RNR (Royal Navy Reserve: men who had been discharged from the regular navy but were retained as reservists - and indeed the novel makes it clear that Ericson had served at Jutland before joining the Merchant Navy), whilst the other officers are RNVR (Royal Navy Volunteer Reserve - men who joined after the outbreak of the war).
At one point, Lt Lockhart removes a tarpaulin to reveal the body of a sailor not out of his teens, awaiting burial at sea. This is a nod to the scene in the book when he confronted with the bodies of several young Wrens (Women's Royal Navy) who die when the ship transporting them to Gibraltar is sunk.
In the book the film is based on, the second ship was a River Class frigate named HMS Saltash, rather than a Castle Class corvette named HMS Saltash Castle. Presumably the change was made based on what type of ship was available for the production.