DCS Foyle's determination to travel to America to take care of some unfinished business refers to the events of Fifty Ships (2003), during which, for purposes of the war, Foyle was forced to release a murderer. The final outcome is revealed at the start of the next series, The Eternity Ring (2013).
The naval officer with whom Foyle discusses his planned trip to America is Commander Howard, his brother-in-law. Howard first appears in season three when Foyle calls a favour in from him.
The name "Jack" plays a key element in this story. As described by James Devereaux, his mother called him by this name as it was the name of James' favorite fictional character. Jack Harkaway was a character in British "penny dreadful" novels - a proper English schoolboy who ran away for a life of adventure at sea.
In the final scene, seconds before the credits, the camera lingers strangely on the uniformed officer who checks Foyle's ticket before he boards ship. This is because the officer is played by Anthony Horowitz, CBE, who created Foyle and wrote most of its episodes.