I don't do a lot of reposting, but this idea of using a pallet as a sort of tiered mulitpot is really smart. I like in particular the fact that you could tilt it, overcoming the problem of plants casting shadows on plants below them. Watering would be tough, particularly in late spring and summer. But it would work very well in the winter/spring period if you were willing to hand-water the lower tiers. I imagine chard and small greens (Tuscan kale, say) on top, mixed lettuce greens below that, then herbs and finally nasturtiums and small, mounding flowers flowing out of the bottom rung. Very pretty, and very efficient use of space.
I would definitely use a well-drained mix, in any case. And perhaps lining the back not with cloth but with a thin plastic sheet, with abundant holes in the lower tiers to encourage wicking downward, then upward.
Adding... Thought about this more. Pegboard and penny nails for the back, that's what I'd use. Yeah, the pegboard would only last one or two seasons, but that's what would work best. And it's cheap, readily available, easily cut. More structure, better water retention.