Hello,
We are re-doing our bathroom (see my post under Renovation:Home Inspector Liable?). What is the best insulation to use for the outside wall in the bathroom? Do I need a moisture barrier? (We live in a cold midwestern state..6 months of snow, 3 months of unbearable humidity).
Thank you?

Absolutely a vapor retarder on the winter warm side of the wall. Depending on the depth of your wall framimg, you can use either R-11 or R-13 fiberglass roll insulation in 2x4 wall framing, or R-19 or R-21 in 2x6 wall framing. The insulation can be supplied with an integral vapor retarder. Just install it in accordance with the manufacturer's instructions.

What is your opinion on using foam board (extruded polystyrene) instead of fiberglass in the bathroom? The fiberglass insulation that I just pulled out was all moldy and damp because it wicked the moisture from the leak. Won't the foam board be more resistant to this?

EXTRUDED polystyrene (usually colored) if far superior to fiberglass as an insulation, especially if there is any chace of moisture. The not use "foamboard" or EXPANDED polystyrene (usually white) that is only good for coffee cups and Walmrt meat trays.

Fiberglass does not absorb moisture, but it physically hold moisture about vapor sized because of the structure and surface area. If fiberglass ever gets wet, it will never dry out unless it is removed and subjects to plenty of heat and air. As little as 1/2 to1% of moisture will cut the insulating value in half or worse.

Extrude foam has a higher R-value if you are into that limited mesthod of insulation and can be adhered to a surface. It can also be cit to size and placed in an opening. If you are concerned about air infiltration (which is not a factor when applied to block/concrete), you can easily foam any joints and be even that much better than fiberglass.

I inspected hundred of homes that had flood damage after hurricane Katrina. When they removed the drywall, it exposed many years of mold growth and rot from the moist climate and wet fiberglass from floor to ceiling despite only a couple of inches of flood water.

Polystyrene insulation will cost many times the cost of fiberglass, and the difference in R value on such a small wall will hardly be noticed. In my experience, despite manufacturer claims to the contrary, foam can act as a partial second vapor retarder, and cause the very moisture problems one is trying to avoid. If at some future date you need to snake an electrical wire through the wall, it will be almost impossible if the wall is full of foam.

In a 2x4 wall, foam will give an R-value of 17.5, compared to say R-13 for fiberglass. It will take decades to recoup the cost of the foam in reduced heating bills, if ever. If your leaks are cured, and your wall is constructed properly, you should not have moisture problems with fiberglass.

That's my opinion. It's your choice.

Thank you very much for all your help. I appreciate it. :-)