What are several elements that make "The Most Dangerous Game" implausible?

Aside from what seems the most obvious example--the
hunting of humans as sport--I find most aspects of "The Most Dangerous Game" to be a
wholly believable tale. Remember, the story was first published in 1924, so some of the
events may seem impossible to believe in the 21st century. Examples might
include:

• A supposedly uninhabited island
  (especially in the well-travelled Caribbean) with a mansion hidden from view. Impossible
  today, but not at the time of the story.


• The incredibly
  coincidental meeting of the two fanatical big-game hunters (but then that's what makes a
  good story--and such coincidences do happen).


• The fact
  that no one ever investigated all of the shipwrecks that occurred off the island with
  the many missing men.


• How did Zaroff continue to restock
  his exotic supplies of food and other luxuries without drawing attention to his secret
  island?