You need to be certain where the water is coming from and address that issue otherwise your drywall will be shot again in short order. Take some pics standing back a few feet as well as from the exterior as you very well may have other issues (water infiltration)

metal framed windows?

http://s808.photobucket.com/user/bettyjoanne1/slideshow/windows
one pic is sideways. All the windows in the house have the same issue. Condensation shows up on 30--50 degree mornings and is not on the windows itself but on the white metal sides left and right. Condensation will form a puddle of water on the window sill. Once wiped condensation will not form again until next 30-50 degree morning.

From your pictures,looks like the exterior trim is installed improperly. It appears the the trim was installed over the siding as compared to the trim being attached to the sheathing and the siding butting up to the trim (siding is also attached to sheathing). This will allow a great deal of air infiltration causing your condensate issues in colder periods.

metal windows condensate.
simple thermodynamics.
heat goes to cold.

in the winter they condensate to the
warm side...inside the house.
in the summer they condensate to
the outside. less noticable as it
dries quickly...because it is outside.

you can try adding a stand alone
dehumidifier to lower RH (relative humidity)
inside the house.
but to some degree the windows will
still condensate.

RH is low in the winter already.

metal is a poor choice for windows because
the metal is very conductive,
when it is cold outside the cold
transfers through the frame...proving
that "thermal break" is next to worthless
with metal windows.

the exception is metal clad wood
windows simply because wood is
not condctive.

I know of people in very high end homes
that live with towels on the window sills
during the winter. and they change the towels
daily.

wish I had a solution for you, but its just
the wrong window frame.

best of luck.

Would filling, priming and painting work to repair? I am trying to avoid having to pull out and then put in new drywall because of the bullnose corners. Replacing to non-metal windows is not an option for another 2.5 years.

The first order of business is making sure the "condensate" is in fact condensate and not windows leaking from the exterior.

If it is condensation, a water resistant covering such as white Corian should be detailed as a replacement for the drywall.

From the amateur appearance of the exterior window trim installation, I question whether the installers knew/did anything about waterproofing.
JMHO

That is what I was trying to get at Randy and why I asked the op for better pictures. Repairing the drywall without addressing the problem is just going to lead to doing the same thing in 6 months and possible much more and worse damage if there is a water infiltration issue.

op clearly states damage is from condensation of all windows.
granted the windows may be flashed incorrectly..all of them,
but if op sees the condensation..then it is pretty clear.

To prevent mold or damage to the interior or dry wall of your home, a good place to start is the proper installation of windows. When a window isn't installed correctly the frame can be misaligned which causes gaps allowing moisture to seep inside your home. Do you still have the same windows in your home? Window