UPDATED on April 8, 2016
There are lots of ways to insulate a low-slope roof, and most of them are wrong. In older buildings, the usual method is to install fiberglass batts or cellulose on top of the leaky ceiling, with a gap of a few inches (or sometimes a few feet) between the top of the insulation and the roof sheathing. In some cases, but not all, there is an attempt to vent the air space above the insulation to the exterior.
It’s rare for anyone to inspect the roof sheathing — unless, of course, the boards gets spongy enough to be noticed when the building is re-roofed. If there were any way you could squeeze into the tiny attic under the flat roof, however, you would probably see evidence of mold or rot.
What’s a low-slope roof? It’s a roof that is flat or almost flat. This type of roof is common in urban areas (for example, on triple-deckers in Boston and row houses in Philadelphia), as well as in the Southwest. Some of these roofs have parapets — perhaps on just one side of the roof, or perhaps on three or four — while others have no parapets at all.
These roofs are either framed with deep roof trusses, or are framed with roof rafters that are separate from the lower ceiling joists (creating a cramped attic between the flat roof and the ceiling). In some of these buildings, the attic is high enough to allow a person to climb into the attic through a hatch; in others, the attic is too cramped for human access.
So what’s wrong with insulating a flat roof the traditional way? Nothing, really — as long as the job is done correctly: that is, with an airtight ceiling and adequate attic ventilation.