A damp mark below a chimney
The front flashing is only one possibility. Side soakers, the rear gutter, pointing and flaunching all need considering.
Water running down an outside wall
Watch the gutter during rain. An outlet blockage may make water spill well away from the obstruction.
A slate has shifted but not fallen
Even a small sideways movement can reduce the overlap enough for wind-driven rain to get underneath.
The loft is wet on a dry cold morning
Widespread droplets on felt and rafters suggest condensation rather than a local rain leak.
A previous repair did not solve the problem
Compare the weather conditions and identify exactly what was changed. A second water path may be involved.