Almost everything worth knowing about a roof can be seen from the ground with a pair of binoculars. Going up to look is where people get hurt, and a domestic roof is not designed to be walked on: tiles crack under a foot and a cracked tile is a new leak.
Walk around and look up
Do it twice a year and after any serious wind. Work along each slope in turn rather than taking in the whole roof at once, because a single slipped tile is easy to miss and is exactly what you are looking for.
Look for tiles out of line, a dark gap where one has gone entirely, and tiles that look lifted at the lower edge. A tile does not usually fall; it slides down and sits against its neighbour, so a run that has lost its regular spacing is the thing to notice.
The ridge and the verges
The mortar along the ridge and down the gable edges is where older roofs fail. Missing sections, visible cracks, or a ridge tile that sits at a slightly different angle to its neighbours all mean the bedding has gone. Those are the pieces most likely to come off in a gale, and they land hard.
Flashings and junctions
Where a roof meets a wall, a chimney, or a different roof, there is a flashing doing the waterproofing. Look for lead lifting away from the wall, mortar missing where it is tucked in, and any patch that has been sealed with mastic as a repair, since mastic is a short-term measure and tells you that junction has already leaked.
Chimneys deserve a careful look. Cracked rendering, missing pointing between bricks and a leaning stack are all worth acting on, and a leaning stack is urgent rather than routine.
Look from inside too
The loft tells you things the outside cannot. Go up on a bright day with the light off and look for daylight coming through, which should not be visible. Look for staining on the timbers, damp or compressed insulation, and any sign of water tracking along a rafter, since water rarely drips straight down and the stain is often well away from the hole.
Do this in heavy rain if you suspect a leak. Finding where water is actually entering is far easier while it is happening.
What to act on quickly
Daylight through the roof, a leaning chimney, a sagging ridge line, or several tiles gone from one area all want a roofer promptly rather than at your convenience. A single slipped tile in a sheltered position is less urgent, but it exposes the felt beneath to sunlight, which degrades it, so it still wants doing this year rather than eventually.
Getting it inspected
Ask for photographs of whatever a roofer reports, which any competent one will provide, and be wary of anyone who offers to reseal or coat an entire roof as a preventative measure. Full roof coatings are frequently sold and rarely the right answer on a tiled roof.