It's been working fine now for a while, and now the issue is back again.
My customer tells me they left some comments. No badge shows on the collection icon. No badges whatsoever are shown on the cells, and when sorting by Last Comment Time, the photos appear in a seemingly random order.
Something interesting to know: this collection had been shared before, customer selected (liked) some photos, and I made it private again (never stopped syncing). The customer asks me to select some additional photos, so I make it public again. They made some comments, and now we're here.
Oh, and of course everything works fine in Lr. Is this a cheap trick to get us to move to the far inferior Lr? no badges in LrC