Vertical farms are a good idea, though when you say organic, do you mean free of synthetic pesticides, or free of all synthetic substances?
I say this because hydroponic vertical farming would be rather awesome.
There's nothing wrong with using synthetic salts as nutrients, and in fact, plants grown hydroponically with synthetic nutrients tend to yield far better (as the levels of each nutrient can be tuned to cater to particular varieties of plant), and are significantly less vulnerable to root rot-like diseases (if H2O2 is added to the water at least, which kills many microorganisms and helps keep the water oxygenated). Larger, healthier plants are more resistant to some of the diseases spread by pests, and the higher yield reduces the impact of losses from pests munching on the plants.
Nothing 'synthetic' ends up in the final product as long as the salts are of decent quality (and if they're not, the chances are the plant will just die anyway rather than produce any contaminated yield).
Not to mention that a hydroponic system would make such a set-up far easier to maintain, with a single tank that can be cleaned/refilled from the ground.