Their felting is messy, and sagging between rafters, it should be pulled taunt.
No double batten at the eaves (1st course into gutter) the eaves slate appears to virtually cover the whole batten, so no idea how they've fixed the first full skate but it's not fixed correctly.
Battens used should be 25x50mm, looks like they've used 38x19mm, check the slate fixings haven't protruded through the underside of the battens into the felt (although I doubt they will have, as the felt is hanging between the rafters!)
Again on the top two courses to the apex, can't see a top batten, looks like the top full skate is resting on the ridge board, if so, where is the cut slate fixed to? Possibly laid loose or masticated to the slate below, with ridges bedded on top.
Probably see more if I wasnt on my smart phone, screen is too small to zoom in on the pics bit I'l be home in an hour sk I'l look more closely then.
Not looking to clever even on this though.