Your system looks great, the only thing can happened wrong is the water distribution in each bucket, the water may find an easy channel throughout the stacking buckets and runs down quickly before wetting the medium in each bucket.
My suggestion is to use a shower head at the top of the buckets instead using drip nosels, in such a way that all the top surface of the upper bucket's medium becomes evenly wet, also make sure to reduce nutrient flow through the system.

If the holes in the bucket are horizontal, How do you keep the substrate and the water from pouring out? If they are angled, how do you ensure the drainage from the bucket above evenly distributed. what is the advantage to this as opposed to a 5 ft, piece of pipe, or several flanged pieces? Don't get me wrong I love the idea of it being modular, just not sure as to the benefits.

Note: just noticed that maybe you said you were going to fill buckets with substrate, if so, seems like a bit of a waste.

Another option, no issues with coverage, no airpump, no water pump heating the res. Can be solar powered with a panel and a battery.

Hex I must try this as I was just sitting down to see how to make a vertical Hydroponic system.

You need a reasonably large diameter tube or the mist wont have chance to develop into a cloud before it hits the wall. The nozzles in the drawing are arranged in a spiral fashion with 90 degree rotation on each, gravity will take the mist down and fill in the gaps.
Unlike the drawing, the plant sites should be staggered on each level so the roots dont align with the plant directly below. That allows twice the distance for the roots to grow downwards before they encrouch on the plant below. With the right mist, the roots will grow down but also out horizontally into the central space to access the mist.