This is the most important problem that you may find with flat or cathedral roofs.
The causes of mold, mildew and rot are typically
roof leaks, or
condensation as a result of air leakage into the roof space.
Damage to structure members is the implication. In severe cases, the roof can loose its ability to carry live loads.
Because there is no access into the roof space, this can be a very difficult thing to determine. Some of the clues to look for include
Sagging or spongy roof surfaces. With practice, you will get a sense when walking on roofs of unusual deflection or sponginess. This can mean rotted or delaminated sheathing.
Sagging plaster or drywall ceilings. We recommend you scan the ceiling surface below flat or cathedral roofs with a flashlight beam parallel to the ceiling to reveal sags. Drywall or plaster that is wet will often sag. A repetitive pattern outlining the underside of the ceiling joists, rafters or trusses may be visible.
Mold or mildew on the ceiling surface. In some cases, the ceiling itself is cool enough to condense air in the house on the lower surface. Mold and mildew may get a foothold here. If this is the case, you may suspect more problems above the ceiling.
Rusted nail heads on ceiling finishes. Sometimes you can see small rust patterns on plaster or drywall ceilings. This usually indicates high moisture levels in the roof space condensing on, and rusting, nails and screws. This should be a red flag.
In most cases, you won't be able to determine whether there is a problem or how extensive it is.