Thanks for all the replies.

To clarify....

The roof has been leaking for over a year. The leak is in the
flashing around the chimney and also around a pole thing they put on
the roof for an antenna or something.T he decking does feel solid
when you walk on it. I have not inspected the attic.

The leak is evident inside. The ceiling has a hole and sags in that
room. At least two walls are also damaged and need new drywall. The
rest of the house does not show sagging ceilings, water damaged walls,
etc. They are lath/plaster walls.

The dripping is from every interior door jamb. In fact, the exterior
doors are the only ones not dripping. I believe the dripping is from
condensation from faulty venting combined with the ongoing leak. I
just can't see that leak running the length of the house when it has
an "out"...the hole in the living room ceiling. I could be wrong.

I figure I'll have remove and replace any insulation as it is probably
ruined and will probably turn into some kind of mold monster in warmer
weather. I do not want it slithering down to get me some hot and
humid night

I have decided not to go with Mr. Cheapo because he is not really a
contractor. Yeah, he is a union roofer and knows what he is doing,
but he doesn't have insurance, or a license and if he does a crappy
job I basically have no recourse.