A salty dick is an old-fashioned slang term for a European residing in the Americas while maintaining dual citizenship both home and abroad. Such a person is said to have one foot on either continent with their genitals dipped in the ocean.
Such a stretch could make anyone crotchety or worse, considering the double responsibilities in terms of taxes and service that go with the territory. And if either of one's countries are ever at odds, the ridicule of one's peers may further irritate the salty dick.
Typically (but not always) British.