There are limits to growth. We are just not anywhere near them, and don't seem to be approaching them. World birth rates are coming down fast enough that world population will probably never again double.
> No limits to available fresh water supplies?
Fresh water is a local problem. The world fresh water supply is renewable and renews at a rate several orders of magnitude greater than human consumption. Fresh water is a problem because transportation of it is expensive, and people prefer to live in places that have supply problems above places that don't.
Still, I expect that fresh water supply problems will mostly be solved by desalinization rather than migration.
> No limits to energy production?
Nuclear is limited really only by capital expenditure. Solar's limits are also vastly greater than any feasible demand, and it's getting cheaper.
> Once you run you of fresh water and have to rely on nuclear power to run the desalination plants to keep people watered, you have three major problems.
And what would those be? In any case, it makes little sense to desalinize using nuclear. Desalinization is a problem that's a perfect fit for solar power, as the capital cost of equipment is low enough in comparison to the energy costs that you can effortlessly vary production with the load, and the end product can be stored well.