I have some moisture (I think from the window AC unit) that has discolored 6 or 7 pieces of the floor right next to the wall and I'm turning the unit over and need to figure out a solution.

It will either suck all the moisture out from the soil underneath the foundation or damage the foundation by growing roots under it. 

If water or moisture begins to leak in through the roof it can reek havoc on the plaster inside.Lesson 2: If there are no cellar doors on the entryway into the basement or some other form of a barrier to prevent rainwater from coming in through the entryway then get new doors or at least a slab of plywood over the entryway to prevent water and mud from entering your basement.Lesson 3: Call at least 1 week ahead of time for ordering materials.

Outside items (like furniture) are subject to expanding and contracting as well as anything subject to moisture or mildew/mold. 

The problems came with these when they were insulated and skirted causing moisture to get inside the cavity and rot the wood and keep the insulation damp.

That means he will likely have plausible deniability for the damage, as he can just claim that his contractors did the make-ready and never informed him of any mold/moisture issues.

If the bottom of the pile has organic matter or household chemicals or anything with moisture, it's most likely damaging the flooring and walls and attracting pests.

The next item on the checklist is the possibility of moisture intrusion through these cracks.

Like electrical, plumbing, and dangerous chemicals.Also while contractors are okay at generating bids, are they going to be testing for moisture in the walls?  

I'm not familiar with Allure flooring, but if it's practically water proof as noted by @Edward Mccracken, then, as he indicated, the moisture is likely collecting from below the sub-flooring (be it a crawl space, basement or sleepers on a slab) and building up underneath the Allure (e.g., waterproof = impermeable).There doesn't need to be visible standing water for this to happen either.