I think building construction on an ocean platform won't be too different from land, advantage is that you don't have land limitations as you can just build more onto the platform.
That being said, i did see a documentary about some skyscraper in India where they had to design it in such a way as to avoid the wind catching it and toppling it over. I'd dare say the same thing would apply when we talk about height.
The main things to consider with ocean platforms involve energy and food, but these supplies can be obtained from the sea.
Solutions: Fishing for food; hydro-electricity or wave generation for energy; water treatment (desalinisation plants) for turning sea water into drinkable water.
The other thing is of cause the sea itself; well yes, you did touch on this slightly when you talked about storms, but also, if the platform is stationary or on a single/multiple pillars these will need to be protected from eventual decay (metal will rust, stone will erode).
Solutions: Pillars made from layers of material that won't rust or erode; consistently maintenance and treatment.
If the platform is not stationary, then how will it handle waves? Small ones might not be a problem, but what about larger ones? If the platform floats then you should also consider whether it will move with the currents and what happens if it approaches land or rocks.
Solutions: The platform can be steered; wave machines produce counteracting waves, to cancel out incoming waves.
Also there's weight considerations; a floating platform will start to sink the heavier it becomes, whilst a platform atop a pillar won't, but that said, how much stress can the platform take with such a big weight on top of it, regardless if it's on a pillar or sitting/floating on the sea?
Solutions: Very think platform which can sink into the sea more; giant walls so the platform can go below sea-level; a dome to cover the top.
Building on the platform won't be all that different than building on land really, it's the building of the platform you should focus on, since that's just man-made land, and if anything happens to the platform then the buildings mounted to it are sunk.