How does a stonefish get oxygen out of water?
I have been trying to find an answer to this question, but until now, no one seems to have really analyzed why this is possible. The only hint I found comes from this paper:


A study of the distribution, habitat, behaviour, venom apparatus and
venom of the stonefish.


They state:


  At periods of low water, stone-fish are often left partially exposed
  by the retreating tide. At such times they may be surrounded only by a
  small quantity of water which fills the depression in which each lies
  and the main mass of water may be a considerable distance away. They
  can survive long periods (at least 24 hours) out of water providing
  their surroundings are kept moist.


Obviously the fish only needs minimal moisture to get enough oxygen. I would further speculate that the fish turns down its metabolism during this time to minimize the need for oxygen. This paper is widely cited as a source for this survival time, but there seems to be no follow up on it. What is widely analyzed is the toxin of the stonefish.