After starting a new campaign, the "build base modus" doesn't disappear after a failed build attempt. as that's the only sensible thing to do. So that's what you can use to find out whether you really can't build a base there. And zoom in on the island.
no point in covering water. destroyed ufos will be lost in water and you wont get any bonus to national happiness.
Well, perhaps you want to reduce the number of tactical missions, or cover already most of the land. It can be useful to keep track of ufos flying over the Atlantic (so you can immediately launch an interceptor when it comes near to the other side).
EDIT
Also, somewhere in this forum it was said that building bases on islands would reduce or eliminate the number of alien attacks on it which come without any warning, that is, without an UFO. However, this seems to be wrong, as I already got such an attack on an island base.