Thought I'd give an update after 2 weeks of ownership.
I kept getting "Battery discharged, start vehicle immediately" and "Battery discharging whilst off" messages. Luckily it never got low enough that it couldn't start, but that was a pain. The dealer replaced the battery with a brand new one on the weekend so that's sorted.
Other issue is the left tail light. I keep getting rear fog light failure warnings (though in reality the fog lights work just fine). The driving light is out and there is water in cluster. Coincidence? I think not.
Dealer agreed to replace it, so I went there on the weekend but the donor vehicle (M235i) also has water in the light, so he is ordering a new unit which I will fit on the weekend. We opened it up to remove the water and found it fairly tarnished inside, water has evidently been there for a while and some of the contacts show signs of shorting, so it's toast. Indicators, fogs and brakes work so at least it isn't completely dead.
I also found the driver's side bolster doesn't work, though the passenger side does. I assumed (and hoped for) a faulty pump so I opened the seats up and swapped the passenger pump to the driver's side, but that still doesn't work. Driver's side pump does work on the passenger side, so it isn't a pump issue. I assume it's a power issue as the pump doesn't react at all when the switch is pressed. My guess is it'll likely be a wiring issue between the main connector, the bolster switch and the pump. I don't have a multimeter so that's something I need to resolve.
And lastly, the dreaded windscreen washers not spraying any water. I can hear the pump trying, but no water comes out and there is an accompanying beeping noise, so something weird is going on but I'm not sure what. Hopefully it's just a blocked line, I'll have to take a look and see what I can find, just ran out of time on the weekend.
Other than that she runs like a dream and everything else works as expected.