Goofs

During the arm wrestling sequence, the old man's shirt repeatedly switches from rolled up above the elbow to buttoned to his wrist.

The boy asks for coffee with plenty of milk and sugar to bring to the old man, yet when the old man drinks his coffee, it's black.

(at around 30 mins) There's a white fishing line extending upward from the marlin as it jumps out of the water, which is impossible because Spencer Tracy is sitting at water level. As explained in the end titles, this footage was obtained when Alfred C. Glassell Jr. caught a record-sized marlin at the Cabo Blanco Fishing Club in Peru.

Although the Old Man is supposed to be way out at sea and all alone, at around 33:00 a small boat with a person on it can clearly be seen between the old man's body and his left arm. Apparently the previous wide shot (Old Man in boat) is reused as background for a following close shot of the Old Man.

After the old man beats off the sharks the marlin has been eaten both below the waterline AND above the waterline. To have eaten the marlin above the waterline, they would have had to leave the water, and that is something sharks would not do.

When the boy visits the old man the morning after returning with the fish, the clouds as he walks up the path to the house are in a certain position. When he returns later carrying coffee for the old man, the clouds are in the same position. The scene was shot without the coffee and then immediately with the coffee.

When the Old Man harpoons the fish, there is a closeup shot of the harpoon entering the fish's body. You can see a bloodied hole in the skin of the fish before the harpoon enters it, as it appears to be a reversed shot.