It's not the islands, it's the salt. Fresh water and food are going to be your primary concerns. Such an environment would be mineral poor as use of any sort of metal would be strongly curtailed, even if found, by the corrosive nature of such a high saline environment.
First, you would need a reason to leave a given island, then you would need to find a way to construct boats large enough to travel. You would be limited to bone tools, trees, vines, and whatever fabric could be woven into sails.
Then, food would be a problem. All food would have to be gathered and shipped along with the people, possibly causing a serious depletion of the source island.
Buoyancy would be less of a problem, as the high saline content would make ships more seaworthy, but the sea itself would be lifeless unless some alien sort of creatures could process that much salt.
Another challenge would be setting up production on the new islands. Ships would have to be cannibalized to create shelters until the new island could be explored and exploited. Finding new food sources would be a top priority, as the sea would not be of any help. again, animal or human bone tools would be the only tools available, and only the ones they brought with them until new ones could be fashioned. There would be no industry to speak of, and the lifespan would be very short due to hard living and no technological progress past a very primitive island lifestyle.