I've just had a re-roof of my 1930s mid-terrace in the UK. The work involved (roughly) the following:
remove all existing slates and ridge tiles
replace horizontal battens and lay roofing felt
put back 'good' slates and replace 'bad' slates with 'good' reclaimed slates
rebed ridge tiles
A Velux window was also replaced.

The only thing that's concerning me is the slates near the joins with my neighbours' roofs. I guess I was expecting a seamless transition of slates as that's how it was before (at least I think - there was a fair amount of moss or something, limiting visibility). Instead there are these small pieces of slate (maybe ⅕ of the width of the others) filling the apparent gaps, only on the left side, front and back pitches. I think these were the areas they worked on last.
I am not a roofer, so I can't really judge whether this is to be expected. Is using these smaller cuts of slate normal practice?
In the image, cast your eye down from where the two chimney flashing pieces meet, and you should should see what I'm referring to. Sorry for the poor quality image; my phone's camera isn't the best. The image might present larger if you right click it, and choose 'Open image in new tab', if you have that option.