There's flat and there's flat. If you're doing a screw for an old high grade (or new) watch that's mirror polished flat you need specific tools and you need to finish on tin or zinc or similar with some sort of paste. Back in the day it was usually diamantine (aluminum oxide), nowadays usually diamond. There's an order of magnitude of effort between pretty flat and shiny and dead flat and mirror finish inspected at 30x magnification. For a case screw 'pretty flat and shiny' is almost certainly A-OK. No need to get freaky with it.
New to watches, I would venture a guess. Since it was behaving as expected for a full 8 days, then started to switch the date incorrectly, would imply something broke, or became misaligned, or loose at day 8.
Obviously I haven’t a clue, but it’s fun to speculate!
would appreciate and update when you figure it out.