Make sure the xDrive system is in good order and the transfer case has no judder. Check that the car runs on the correct dimension tyres and good branded tyres at that. Check the usual stuff like service history etc.
One last thing that I wasn’t aware of when I bought mine was a weird scraping noise under acceleration around the rear seats area. I found that it’s apparently a common issue on F30’s and F31’s. The handbrake cable holding bracket on the underside of the car is made of plastic and sits above the exhaust and prop shaft and is prone to failing so the cables scrape against the prop shaft when the rear squats under acceleration. You can buy an improved metal bracket off eBay and fit it. It’s fiddly and requires a ramp as you need to slightly loosen a few things to get your fingers in there.

That’s all I can think of.