Factual error: The fact that the respiration of a single animal - however large - could lead to an increase in the level of carbon dioxide in the local area is so absurd it is laughable. Carbon dioxide exhalation is part of a closed loop cycle and the CO2 exhaled by Kong would be matched by the CO2 taken in by the plants growing on the island. It cannot be otherwise. Elevated levels of carbon dioxide are incredibly dangerous and any animal living on the island - including Kong - would suffer if things got out of kilter.
Factual error: How does Kong return a radar signal? If organic material is suddenly detectable by ship borne radar, why isn't it picking up the trees and other animals? Did someone invent gorilla-detecting radar?
Continuity mistake: At the beginning when Dwan is tied to the podium and waiting for Kong she looks up and the trees are moving with Kong's presence. Then we see Kong approaching through the woods from a distance.
Answer: He probably knew it wasn't deep. It's his island; he knew every inch of it. Besides, it's a pool, not an ocean. It most likely had a small underground tunnel which spilled out somewhere on the island.