Flashing failure
Ask anyone who repairs roofs where they leak and the answer is the same: not in the middle, but wherever the roof meets something else.
Step flashing along a wall
Where a roof plane runs into a wall — most commonly along an attached garage or a second-storey addition — individual metal pieces are woven in with each course of shingle. Done properly it is invisible and lasts as long as the roof. Done as a single continuous strip sealed with caulk, it fails within a few years when the caulk cracks.
This is also the item most frequently re-used rather than replaced during a roof replacement, and it is the most common reason a new roof leaks in its first year.
Chimneys
A chimney needs two layers: base flashing that goes under the shingles, and counter-flashing set into a groove cut in the mortar and folded down over the base. Where the counter-flashing has simply been surface-sealed to the brick, it is a matter of time. Older masonry across this region has frequently been repointed at some stage, and the flashing detail does not always survive it.
Vent boots and skylights
The rubber collar around a plumbing vent stack is the shortest-lived component on most roofs. Fifteen to twenty years of ultraviolet exposure cracks it, and water runs straight down the pipe into the ceiling below — often appearing in a bathroom. Skylights leak at their own flashing kits, and a skylight that is older than the roof around it is worth looking at closely.