The smell you have can be from many factors. To understand what is going on you must understand how a mildew odor is created.
Any mildew/mold smell requires three items to develop. A food source, air and moisture. Knowing this and understanding you can only control the moisture side of things we must look at where this moisture is coming from.
Now you suspect the brick veneer is the issue. You say that the contractor put behind the brick Tyvek and that the contractor placed weep holes, and flashings. Is the flashing located at the floor sill level or is it below that point below the surface of the grading? The weep holes are placed on top of this flashing. Is the brick spaced off of the house framing at least 1/2 inch from the wall? Did they clean out behind the brick when they place them? Or did the contractor allow the mortar to squeeze out and come into contact with the Tyvek covered wall?
My thoughts on this even if they did install the walls properly or incorrectly this is not the source of the moisture.
We need some more information. Where are the rooms located within the house. Basement, first floor, 2nd? I assume they are next to the brick veneer side. Which way does the room face? North, south etc?
What kind of heat to you have? AC system installed? Overhead or in walls with air ducts?
Do you have plastic runners, on floors? What about carpets? If you have them does the sun shine onto them through the windows? What about drapes? What are they made of or do you have plastic blinds?
What part of country do you live, USA or other country?
How long has this odor been taking place? Recently or sense the house built? Did it seem to appear after you perhaps changed the look of the rooms in question? What do they have in common. Are they next to each other, or do they just face the same way and are in different locations in the home?
Reason for these questions is that many of the products we fashion our homes with contains many man made chemicals. These chemicals out-gas all types of odors. If the sun shines on some of these materials they can give off smells that mimic mildew and mold.
leaking brick walls which results in moisture and odors would happen pretty much all year round. Moisture does not stop just because its winter out.
Recently there has been some issues with the wallboard that was installed in many of the homes down in the southern states. It appears that due to the hurricane a few years back they ran out of the stuff for construction. They began to import a lot more drywall from China then they did in years past. It appears that this drywall contained some pretty nasty things that have been giving off some strange smells.
If you suspect that your home contains this material I suggest you visit the web site
http://chinesedrywallcomplaintcenter.com/ to find out more.
Answer these questions and perhaps I can offer some advice on what way to go.