Unfortunately, I've had consistent problems with our Dodge Grand
Caravan's windshield leaking at the top. After some attempts of repair
by the dealer and the a local auto glass shop (by back filling), I had
the shop replace the windshield.
Over time, a leaking windshield will cause the pinch weld on the body
to rust (see Stubby's post above). This can be a major problem as the
windshield provides a fair amount of structural strength to the
vehicle. This is where a body shop may have to be called upon.
Good luck, as this can sometimes be difficult to fix, even with the
nessary body work and new glass.