There is third person omniscient and third person limited point of view. In omniscient, the reader has access to many points of view from many characters. The reader can gain knowledge of many things that one character could not possibly know. The third person limited is where the reader follows one character around. The advantage is that the narrator might be more observant and the reader can 'see' more however, they are limited as to what one character can see or experience. Another advantage of third person limited is that the reader can have more objectivity and what they see is filtered through one character. However a disadvantage would be that the reader is distanced from the emotional life of the character.
This story is told in the third person omniscient point of view. The narrator is not a character in the story, but he is an objective observer who tells the reader the thoughts and feelings of most or all of the characters in the story.
The advantages of this kind of narration is that it provides a wider perspective from which the thoughts of the old man and the other characters can be presented. At the beginning, we not only know what Santiago is thinking, but what the other fishermen think of the old man. The third person narrator is usually a more reliable narrator than first person since the reader knows the other characters from the narrator's perspective only.
One disadvantage of the third person point of view is that the reader isn't able to make as personal a connection with the narrator as he/she can if the narrator is first person. Since a character in the story tells it in the first person point of view, the reader gets to know that character well, providing the opportunity to empathize with him/her more. First person can also make for a better story sometimes if the reader doesn't know what the other characters are thinking. Edgar Allan Poe, for example, chose such interesting narrators for his stories. Reading "The Cask of Amontillado" or "The Tell-Tale Heart" from the narrator's point of view helped to create the eerie atmosphere needed for his gothic literature.