There is a spot north of Jiguey (around 583,601) where a white whale jumps out of the water every time I'm sailing through there. The game, however, never says anything about it and I can't initiate the harpoon mini-game.
I've read that white whales are social events and that they get shared. However, there must be non-social white whales, right? The "Legend" section of the map lists both a white icon and a blue one for the white whale. The same goes for chests and naval convoys.