I'm gonna step out on a limb here, but I'm pretty certain this is not mold or mildew you're dealing with. And, for the record, it's impossible to say, with certainty, what the problem is just from these pictures. My personal guess, is one of a couple things. #1 is efflorescence. Efflorescence is often times seen on bare or painted masonry or cementitious surfaces (concrete, plaster, plasterboard, patching plaster, etc.). Efflorescence are soluble salts, brought to the surface via moisture or vapor transmission. This moisture may come from a damp wall or simply from the application of paint itself. Efflorescence may show up as a white stain or haze, or even as a thick, crystallized, powdery, chalky, dusty clump on the wall. Treating efflorescence is fairly simple (although if it is caused by moisture from a damp wall, that needs a different kind of attention). To begin, it may not be a bad idea to lightly scuff-sand affected area to break through paint film. To treat, mix a 50/50 solution of white vinegar and water and spray onto affected areas with a spritzer bottle - then allow to sit a few minutes. During this time, you may or may not see the white deposits effervescing - if so, wait a few minutes and repeat until the bubbling stops. Wipe affected area with a damp sponge, then rinse the area with clean water to neutralize..Allow to dry, then repaint.
#2 - May be paint frosting. If this is the case, the treatment may be a little more involved. Frosting is usually seen on tinted paint, often times in darker colors (only because the frosting isn't as visible on whites and lighter colors), and is the result of tinting bases containing calcium carbonate as an extender pigment (calcium carbonate is a common extender pigment used in most latex paints). The frosting may occur for a number of reasons - paint has too great a cc load relative to the amount of resin, atmospheric conditions at time of application, extreme temperature shifts during dry and/or curing time, humidity, etc. Frosting may be easily removed by just washing with clean water...and hopefully that'll be the extent of it. If it's more stubborn than that, do not paint over it thinking that'll take care of the problem - chances are, it'll bleed through an additional coat(s) of paint. In extreme cases (and I don't think we're dealing with that here), it could actually have an impact on adhesion of subsequent coats of paint applied. If the case is extreme and can't be simply washed off, it'd be a good idea to lightly scuff-sand the affected area, then prime with resinous, masonry type conditioner before applying finish paint.
Finally, if this were mold - don't panic - you already know the treatment for mold. Mold is not some sinister entity with evil intent. It is simply plant life - and it can be killed. The difficulty is the fact that what you see is not necessarily the extent of mildew. If mildew is in previous layers of paint, or underneath wall covering, and all you do is treat the surface - it may not be that successful. We live with, and breathe in, airborne mildew spores constantly - some people have allergic reactions to it, most don't. Mold, like all plant life, needs certain things to grow and colonize. Mold doesn't do as well in sunny or dry areas, so damp and dark areas should be monitored...Mold also needs a food source - which can be anything organic. Sometimes paint contributes to the food source - alkyd paints have an organic element that mold and mildew feed on - latex, specifically acrylics, not so much, but any paint tinted with organic colorants may provide food source...some organic cleaning compounds leave a residue that may be food source. When cleaning a surface affected by mildew, it's recommended that a bleach and water solution mixed into a detergent is usually appropriate. Stay with non-sudsing detergents such as Soilax or Dirtex Powder...Detergents like TSP, contains phosphates which is a fertilizer to plant life. Without adequate and proper rinsing to remove any detergent residue, TSP could actually create more of a problem.
I hope this info is more helpful than confusing, let us know what happens.