Going back to that wobbly wall issue. In your picture you have looks like 1x4's laying flat across the 'top' of the pallet wall. I would take those off and replace (the full length all walls) with a 2x4 screwed in. Saw a picture of this a few minutes ago, I will hunt around and try to find it again and post link. If I were building this way I would actually do the same treatment on the floor as well, so the base of your pallet wall would be screwed into a 2x4 instead of the pallet floor, and then the pallet walls topped with 2x4's also. This would raise the height of your wall 3 inches. Too late for you to put a 2x4 sill down like this, but you can certainly top your 'walls' with it. Seems to me it would take care of that wobbly issue. I'll look for the link...I really like your progress so far.
To respond to the guy questioning the actual savings using the pallets as 'framing' ( and I don't mean this in a flaming way at all), you raise a valid point. It all depends on how dedicated you are to saving a buck, you can use pallets for 100% of your coop (walls, 'studs', siding, roof rafters, roof boards, etc.) and save a bundle. I am doing exactly that. Some people use pallets as 'structure' or framing for walls then use conventional siding as you mentioned, but some use pallets for most of the structure. If I were building using Flyboys method and trying to save the most money possible, I would not attach siding over the pallet walls, I would fill in the gaps vertically by tearing some pallets down and ripping them on the tablesaw to fit the gaps left between the pallet boards. Some question the extra time and effort it takes building with pallets, worth the trouble? For me it is, I have plenty of time and sort of challenged myself to build not just as cheaply as possible but DIRT CHEAP.