The Self Build Self Help Site roof design
A few other things of note:-

Lead flashings

Ensure you treat the lead of the cavity trays (or lead flashing where cavity trays cannot be used) and soakers with patination oil. This seals the lead and prevents oxidation which leaves unsightly whitish stains on the lead. It isn't vital, it will not cause any problem, but its a matter of the quality of the finish. It is best to treat the lead before the cavity trays are built into the walls and the soakers are added. A coat of oil afterwards treats any parts that have been scuffed.

Dressing the Verges

The tiles at the verge can be finished off with a dry verge system whereby the edge of slates are covered with a continuous strip of plastic or tile length units for concrete/clay tiles.

These systems will prevent rain from being driven through the tiles ends without the need to use mortar (the underlying membrane should still channel water to the eaves).

Some people prefer the look of these systems, others prefer the neatness of the tile/slate edges themselves.