Some people worry about flat roofs, but I never do. I don't see what's the big deal. You cover them with some sort of membrane, whether "rubber" (not really rubber, but a synthetic material called EPDM) or "torch down" (modified bitumen, similar to asphalt and heat-adhered to layers of fiberglass) and as long as you seal the edges properly and don't puncture the roof, it's good for a long, long time...
Upon a quick first inspection of this house, it seemed that the main roof was in decent condition (there was absolutely no evidence on the inside of it EVER having leaked). However, the roofs on the cantilevered overhangs between the 1st and 2nd floors were another story. They had been coated and recoated so many times that they were best described as "gunky" and Joe the contractor described some parts over the porch as "spongy". Not being an expert on roofing by any means, I started contacting roofers to appraise the roof's condition and give me an estimate for the recommended work.
Much to my surprise, no two roofers gave me the same advice and their prices for the work they deemed necessary ranged from $1,200 to $12,000 (!), and from "just apply some silver coating to the various parts and call it a day" to "you need to reconfigure the roofs, apply new roofing throughout, and install new gutters all around"... While some thought a new "torch down" roof was the only way to go, others said they wouldn't consider anything but "rubber"... And several wanted to secure the new roofing material with the dreaded "termination bar" on the face of the overhangs (the cheapest and ugliest thing ever!)...
Finally, the plumber recommended a friend of his, Michael, to do the work. Michael had a compromise approach (in both work and price). He said that the top roof still had a lot of years of life, so he suggested re-adhering any roofing that was loose along the top of the parapet walls and silver coating the entire thing. (Note to self: Remember to tell whoever buys the house that they should silver coat every five years - it will extend the life of the roof and reflect the summer heat).
For the overhangs he had a more radical approach. He suggested stripping them down to the original sheathing and applying a new torch down roof using the original custom-made drip edging. So, this is what we decided to do.
In stripping the overhangs, he uncovered a bit of Pittsburgh history: the original "coal tar pitch" roof (coal tar pitch: a by-product of processing coal into coke). Unfortunately, on the front overhang, under all that pitch, he discovered some rotted wood. With rain being predicted, Joe quickly replaced fascia boards and sheathing and Michael finished up. In hindsight, I should have taken that opportunity to give the overhang a bit of a slope and add a hanging gutter all around. But, in the rush to get it recovered before the upcoming rain, I just didn't think of it. Maybe when this roof wears out, whoever owns the house then can do it... 
The roofer then replaced the drops that connect through the overhang structure to the downspouts and installed a torch down roof with the proper edgings and flashings, thereby maintaining the look of the original house. On the main roof, where most of the water ends up, he secured the parapet roofing, silver-coated the entire thing and installed a gutter that wrapped around the overhang. And, the overhang roofs: Wow! They looked great, What a difference from their old gunky selves.
A day later, after a heavy rain, I was giving a tour of the house to some folks, and much to my dismay there was an inch of water on the front overhang! I was sick to my stomach! All that work and money! It seems like the front overhang has sagged a bit over the years and the water just doesn't get towards the drop (and, therefore, the downspout) as it should. What to do? Just the kind of thing that keeps my brain churning in the middle of the night for hours on end...Fortunately, Joe has put me at ease - his own roof holds water that and he's never had problems. So, as long as the membrane is intact and gets silvercoated periodically, it's ok for it to hold water (some of the roofers had said that; others said absolutely not). But, just to be safe(r), I'm going to have Joe install another drop and downspout on the opposite end from the existing. This should let the majority of the water run out and we should be ok. However, I'm not happy about how that extra downspout is going to look :-(
