Highup - You were asking about the screws. They are called ITW Tapcon 24165 - 3/16" x 2-3/4".
Jon - In Canada, the concrete in the basement is really cold so in the absence of in-floor heating, we will laydown a moisture barrier like the Delta FL along with plywood before installing the engineered hardwood. This creates a bit of an insulator.
The hole is barely larger than 1/8" so no way is any cement product going to get forced all the way down to the bottom of the hole. With that small of a hole (5/32") spaced 16" apart, I don't see any real structural integrity issues with the slab either. If they were 2 inches apart, and in a straight line, maybe.
Lets assume there is some rebar in the slab............ the slab isn't going to crack and separate or move apart. The building inspector is correct about the intentional cuts that are sometimes put in slabs as 'control' joints. They make concrete crack
at those points instead of randomly. Concrete does crack. If the concrete forms a hairline crack
because of those small drilled holes, it's because the concrete was stressed and wanted to crack at that location anyway.
The concrete isn't going to crack and turn into gravel, so personally, and if it was my place, I wouldn't worry about that issue at all.
You see the drawing I sketched earlier? That was how it would actually look
before the plastic dimple board and plywood was installed.
The concrete is drier at the top, because of the constant evaporation of moisture into the room.
Shown here, the plastic and plywood is installed. The moisture can't evaporate anymore, so the moisture content in entire thickness slab builds up and becomes more or less equal. The only real issue I see, is the lack of sealant which would stop the moisture
vapor from slowly coming up above the top of the membrane.
Remove the screws, vacuum the hole, apply sealant to the screw and unto the hole, then install a 3" screws?