Actually, doing the insulation that way with the plastic on the back and a vapor barrier on the front will be the actual CAUSE of the moisture forming, and WILL trap the moisture between them. The plastic is a vapor barrier itself, and very effective. The paper vapor barrier on fiberglass insulation is also effective but not as much. It's porous compared to plastic, plus no matter how neat you are installing the insulation you cannot possibly make it so there is no entry point for moisture or warm air to get behind it. What causes the moisture is when some warm air hits a cold surface inside the wall. Warm air will go through the tiny openings where the paper has folds in it. It will then be in contact with slightly, or much more so even, cooler surfaces such as the studs themselves or the plastic near the concrete wall. It will condense into actual water droplets. Moisture will certainly make it's way into the wall through this barrier in this manner, but not all of it will make its way back out. This is where the mold comes from. Anytime you build a wall, you want just one vapor barrier. Never two. You'll run into guys who say they do it this way all the time and never have problems. But think about this.....how do you know you have problems until you either can't breathe well anymore, tear it down again, or else wait until it's so bad that it finally shows on the wall itself, which when that happens it's 50 times worse inside the wall than what shows through on the outside.
One vapor barrier. One only. You can use the plastic on the back side, then the insulation that does not have a vapor barrier in between the studs. Cover this with your wall covering and be done with it. Fiberglass insulation is good but nothing beats sprayed in foam. This is waterproof, non porous, seals the gaps, and has even more R value to prevent warm air transfer to start with. Fiberglass with a paper vapor barrier will let warm air slowly transfer into the wall and contact cooler surfaces for this condensing process to begin, and mold soon follows. You just can't seal it so well that this never happens. It will also transfer into the wall with just the plastic on the back as well, and even condense, but without that second vapor barrier it will evaporate much easier and at least greatly slow down the molding process. Personally I wouldn't use fiberglass insulation in a basement. Basements are cool, damp, sometimes dark places. Perfect for mold to grow.
