While walking the streets of Seattle in the movie, James Caan is approached by a panhandler who asks him for change. The man was an actual panhandler who didn't see the cameras on the street, and mistook Caan for a real sailor.
James Caan appeared six years later almost identically in sailors garb for an uncredited cameo in Steven Spielberg's 1941 (1979) as the sailor who throws the first punch in the ballroom fight sequence.
"Cinderella Liberty" is Navy slang for temporary absence from ship or station, which ends at midnight on the last day. Typical periods of liberty are 24-72 hours.