Basement – Installing in-wall speakers in an exterior basement wall

No, you only want a single vapor barrier. A second vapor barrier would create a moisture trap that would cause more mold issues. If there's a condensation issue, I'd replace the section of HVAC ducts with an insulated duct. The insulation inside the duct prevents the outside metal part of the duct from getting cold enough to result in condensation.

Ask yourself this: "If I install a vapor barrier, where is the water that it stops going to collect?"

If you put a polyethylene vapor barrier behind a drywall-covered stud framed wall, then the answer is that water that condenses on the poly will fall onto the wood sill plate, growing mold and eventually rotting it out.

Dedicated vapor barriers have no place in a basement wall. If the basement wall is insulated on the outside, then the vapor barrier is superfluous; otherwise, is it dangerous, as it will trap moisture against a moisture-sensitive element, as I indicated.

Here's lots of supporting evidence, since this perspective appears to be controversial. From http://www.greenbuildingadvisor.com/blogs/dept/musings/how-insulate-basement-wall

Should I include a polyethylene vapor barrier?

No. Basement wall systems should never include any polyethylene. You don’t want poly between the concrete and the insulation; nor do you want poly between gypsum drywall and the insulation. You don’t want poly anywhere. Paul Ellringer, an energy and mold consultant in Saint Paul, Minnesota, has a collection of slides showing moldy basement insulation. In most cases, these basement walls were insulated with fiberglass batts, and included two layers of polyethylene — one on each side of the studs. Ellringer calls this a “diaper wall,” and reports that most of them are a mess. “Fibrous insulation and poly are inherently problematic, and should not be used in below-grade walls,” says Ellringer. “Sometimes when you open it up, the fiberglass is soaking wet. If the house is two to four years old, the studs are often beginning to rot.”

And from http://www.buildingscience.com/documents/information-sheets/basement-insulation:

No interior vapor barriers should be installed in order to permit inward drying.

And from http://www.buildingscience.com/documents/digests/bsd-103-understanding-basements/:

Unfortunately, locating insulation layers on the interior often conflicts with the traditional approach of foundation water control – namely inward drying. Constructing frame walls, insulating the resulting cavity and covering with an interior plastic vapor barrier is common (Photograph 2) and often leads to odor, mold, decay and corrosion problems (Fugler, 2002; Ellringer, 2002). Also common, and prone to similar problems, is the use of “blanket insulation” often derisively referred to as “the diaper” for the odor problems associated with the approach (Photograph 3).

If you have not yet constructed your stud wall against the existing basement wall, please read those links to find out how to do it safely and properly.