The title is a play on the title of Ernest Hemingway's novel The Old Man and the Sea as well as "The Big 'C'" being a common euphemism for cancer.
A reference is made to canine cancer detection, the ability of dogs to smell the alkanes and aromatic compounds generated by tumors.
Carter asks Lois if she is challenging him to a Brewster's Millions. This is a reference to a film of the same title, which involves a challenge to waste money.
Two of Carter's phony coffee orders at Starbuck's are for "Beany" and "Cecil". This refers to characters from the 1949 puppet show created by former Warner Bros. supervisor Bob Clampett. Beany was a cherubic little boy who would have spirited adventures with his friend Cecil, a great green friendly sea serpent.