Home inspectors do not begin examining a roof with a flashlight in the attic, but rather on the ground outside the house with a pair of binoculars. These are not lazy or fearless people (if the latter is true, then they made a very bad career choice); they're looking for obvious signs of trouble, like missing shingles or holes made by animals, as well as standard red flags, like skylights and plumbing vents. They then check the attic for any signs of water and double-check all the trouble spots noted during the ground inspection.
If you see water damage on your ceiling, don't assume it's caused by a hole in the roof directly above. It could get in just about anywhere and wind its way down the underside of the roof deck before it falls onto the back of the ceiling, thanks to gravity and liquid adhesion (yes, there's a name for that). You can sleuth your own leaks by starting outside, then going to the attic with a flashlight.
Here are 7 obvious trouble areas to look at: