Should I put a moisture barrier between a single ply of pressure treated (PT) plywood and a second non-PT ply when constructing a shed

I don't know about the cedar, but I built a screened porch a few years ago using standard PT lumber for posts and railings and painted it with a coat of primer and a coat of exterior latex pretty much as soon as it no longer appeared damp. Of course the 6X6 posts had been up and drying for a while at that point, probably 6 months or so. The railings were installed last and were probably only up for 2 or 3 weeks when they were painted. When we moved from that house earlier this year there were no problems with the paint, and that was after about 2 years.

Interestingly, the only paint-related issue we had was some peeling on the existing deck railings, about 4 years old and never painted at that point, that I painted at the same time to match the new railings around the porch. I have no idea what caused it, but I can say that I didn't prepare this older wood at all and it probably could have used at least a good pressure washing prior to painting.

I completely disagree with BMitch here. If you live in an area with sustained freezing temperatures, you should have a plastic vapor barrier between the drywall and the studs, wherever "warm meets cold" (exterior walls, top floor ceiling). You want this vapor barrier inside your insulation so the barrier is toward the "warm" side of the thermal break provided by the barrier, thus reducing the amount of condensation that forms on it.

Paper, like the backing of your insulation rolls, is NOT a vapor barrier. Neither is the insulation itself, even though its purpose is to "trap" a bubble of air and thus provide a buffer between warm and cold. Neither of these are continuous; the insulation is cut to fit inside the studs, and so air and thus moisture can still get around the paper. Moisture also soaks into paper. 6-mil plastic vapor barrier, installed properly, has no way through it; it's sealed against the studs so the drywall screws don't break the barrier, and all J-boxes are sealed with Tuck Tape or similar vapor-proof adhesion.

As for mold concerns, there shouldn't be any, even on the back side of the wall. Because the area behind the vapor barrier can still breathe, even with the insulation, there is little chance of there being enough water in the wall to damage the studs or cause mold to form on them. The big concern is the drywall, which is a sponge for any condensation that may form on it. It will trap this water and hold it for a long time, which along with the processed wood product (paper) on its skin, is a definite attraction for mold.