If the paper face was put to the outside the water vapor in your bathroom was getting into the insulation and condensing. I would pull out the inulation and check for rot and water damage in the wall. The best thing to do is pull out the insulation, let the wall cavity dry out repair any water damage areas. Then replace with unfaced insulation and cover the wall with 6 mil or 8 mil plastic. seal all the edges with tape used with plastic and seal the edges of all penetrations, ie outlet boxes, etc. You want an unbroken vapor barrier. You should gut the entire outside wall(s) in your bathroom and remove the insulation and replace the vapor barrier. I just hope the water vapor penetration did not do too much damage to your walls.

First, the tuck tape. Look for "sheathing tape". It's usually sold in the box stores, sometimes it's red colored. You could use Tyvek tape as well. The vapor barrier is a bit tougher to diagnose. Your exterior foam, "expanded polystyrene" is usually quite leaky with regards to moisture transmission and is not a strong vapor retarder. "Extruded polystyrene" is a much tighter product, and it could indeed be a vapor barrier, probably a Class II barrier. If the exterior foam is indeed continuous on the walls and well detailed, then it might be best to omit the interior poly and just use the Roxul. Your walls may take in some vapor over time, but the vapor should also transmiss back into the bathroom during drying cycles. The biggest problems occur when you have two barriers and one or both are poorly detailed. Over time moisture gets in but has difficulty getting out. Thus the "sandwich" that you referenced. The "imperfect" in your system is the exterior foam. I'm a proponent of foam, but only if it is the right type and the proper thickness. With your exterior foam probably being a Class II on the exterior side of your wall, your best bet is probably to omit the interior poly and simply use other methods on the interior walls. You can use something like Hydroban in your shower (if the shower is on an exterior wall), it's a waterproof barrier but does allow vapor to transmiss through it. For the remainder of your walls, simply use two coats of latex paint over your interior drywall. Latex paint is classified as a Class III vapor retarder. As such, it'll slow moisture vapor transmission that wants to get into your wall, but if any does, it'll allow your wall cavities to dry out during a drying cycle. It's an imperfect solution for an imperfect situation. I'd be completely confident in my reply were your exterior foam thicker than it is and if I knew it was well-detailed. My concern is the interior side of the foam reaching dew point temperatures in winter and any moisture vapor within the framing cavity condensing on the interior surface of the foam, between the foam and the sheathing. That may not be a problem. But it is a consideration, especially since I tend to go towards the conservative side with an "over the internet diagnosis" such as this one. I'd certainly do more research if you can, you might get better information than what I'm offering. You are addressing moisture generation within the bathroom. That's good. Other stuff: 1) I do sometimes insulate interior walls, Roxul is good for that. 2) A simple yet effective sound deadener behind your washer and dryer is nothing more than a second layer of drywall over the first. 5/8" is better than 1/2" due to the added mass. Beyond that you can go fancier: 2a) sandwich a 1/2" sheet of homasote between the two layers of drywall. 2b) Use RC clips and metal channel between the studs and the drywall. 2c) Use green glue between the two layers of drywall. 2d) If you do research you'll probably see references to mass loaded vinyl, but I usually use that only when doing fully integrated sound deadening room "systems". I think you'd do better (and save money) with just using drywall.

For interior walls where there will be no poly, no need to slice the kraft. These are the walls where you're using it for sound deadening. On the wet shower walls, or any exterior walls where you'll also have the 6-mil poly, yes, take a utility knife and slash the kraft facing. You only want one vapor barrier in a wall assembly. If kraft, then just kraft. If poly, then just poly. If kraft and poly, go Anthony Perkins and slash away at the kraft. Mongo

Exterior walls are always insulated, interior walls aren't. However, there are some who wish to have some sound dampening. As noted, regular insulation won't really do that, but there are products and techniques that do accomplish that goal. I put QuietRock on the bedroom side, next to water walls in bathrooms. It doesn't soundproof but will reduce noise transfer. Other systems are available, depending on your needs.