Vertical/wall garden is one of my back burner projects. So I haven't built one yet, but I spend some time thinking about how I would like to build one every year,
How to support and hold in the growing medium would be one consideration, of course. Something that is moisture retentive. I think I'm going to use a roll of coir liner sheet some how -- I want to grow edibles so I don't want to use synthetic materials like landscape fabric. I've considered a simple twin wall wire fencing/CRW/cattle panel separated (at least 6" apart) by cedar/redwood etc. dimensional lumber and end posts. I don't know how long a wooden pallet would last... I don't want it to be crumbling after one season UNLESS it's a simple construction.
The necessary constant moisture levels means you need to consider what it is going to stand against -- if wall or fence, will it resist water damage, what kind of vapor barrier is needed to protect? If air circulation is needed between the vertical garden and the supporting structure, how to create the separation while providing sufficient support? Can it be free-standing despite own weight and wind pressure?
Choice of plant matter -- upper levels will be most drying and sunniest while the lower-most levels will remain wettest and be most shaded by the upper foliage. Suitable theme for the garden with the constrained plant choices?
To support and maintain moisture levels for the upper-most plants, no matter how drought resistant, some kind of regular watering is needed. At minimum daily manual watering, but probably automated drip type would be better. I was considering a perforated gutter or pipe/hose (not soaker) along the top and a catch tray gutter at the bottom with a reservoir and a pump for circulation. (Actually my GRAND plan is to tie it into a system with a rain barrel or pond....)
...I've also looked at hydro and aquaponic vertical garden designs using series of connected gutters, pipes as well as vertical hanging pipes/posts with filter media.