Datarebal, see attached photo of some of the newly-installed slates.
Woody, that's good advice of course, but depends on me having the technical knowledge of lead codes, flashing installation techniques, and slate roofing, to be able to spec the job beforehand, or to challenge them afterwards. Most people (including me) don't have that knowledge - which is why we have to trust tradesmen, check reviews on them etc beforehand (which I did). I have learned more (quickly!) after the job was done - perhaps I should have done that research earlier!
Anyway I asked them again about the lead code (open question "Remind me what lead code it is?") and they immediately said code 4, so if there's no foolproof way to verify after installation, there's not much more I can do. If there's no way of telling, lead manufacturers should imprint a small code number every 90cm along the lead, to ensure that there will always be one number on every sheet, since the minimum sheet length is 1m.
I asked about the flaky tiles, they said that they were reclaimed Welsh tiles to match the colour of the existing old tiles, or else they would look odd, and that older tiles do have a level of flakiness but it was only minor and wouldn't affect the weatherproofing.
They said they'd cut the old lead out of the gap between the bricks (but left the rest of the sheet in place), and installed the new lead sheet into the gap to a 35mm depth using clips, and mortared it in place.
So I'm going to leave it, as it all seems "probably" OK - but chalk one up to knowledge and experience.
Thanks again for your help!