Revealing mistake: When Kong first shows up to take Dwan away, he roars and pounds his chest. As he does so, the breastplate in Rick Baker's costume vibrates visibly in a way that a flesh-and-blood chest wouldn't.
Revealing mistake: Near the end Kong rolls off the top of the World Trade tower. It cuts to a shot from the ground looking straight up toward the top with Kong falling downward. For a fraction of a second there is no image of Kong composited into the shot: first there's just buildings, then suddenly Kong appears from nowhere in midair.
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.