Continuity mistake: When the old man goes out fishing, after 84 days with no luck, one of his four lines catches a fish, but the fish drags the line out of the black ring, which it was tied to, but when the old man goes to the rod, the line is still there - which it shouldn't be.
Continuity mistake: After the old man has brought his fish in - really only the skeleton, after the sharks and other fish have devoured the fish - he goes straight to bed. The next morning, the boy goes to the bar and asks for coffee, with milk and sugar. But when the boy pours the coffee into a small tin cup, it is black, not a drop of milk to be seen.