I agree that the problem probably stems from excess moisture and that a dehumidifier will help. However, it might stem from poorly insulated plumbing that is causing condensation in your ceilings, leading to mildew. It also might stem from a water leak from upstairs. If so, the dehumidifier will not help much because the moisture problem is inside the ceiling, not in the room. It also might be a combination: a water leak that was fixed years ago started the mildew, and the high humidity allows it to continue and florish.
Fundamentally, you can cover mildew up, but the only way to get rid of it is to rip apart the ceiling and kill it with bleach, then use those stain-covering primers and mildew resistant paints. Rumor has it that mildew-blocking primers such as "Kilz" will kill mildew, but that is a lie that not even Kilz claims its own paint can do. Kilz "kills" the stain from dead mildew, not the mildew, itself. Mildew resistent paints can merely allay mildew, even when boosted with mildicide additives. You need to get rid of the pest before mildew-resistent paint will help.
Check out the following links I found researching mildew:
[This message has been edited by Lawrence (edited December 06, 2000).]