Service history is a big one. The car is ten years old so should've had the brake fluid and coolant changed 5 times by now, and ideally more than 2 oil changes. Anything that feels or sounds suss in the driveline could be a problem: the 02 coopers had dodgy manual and auto boxes. If the fluid is changed they can last quite well but BMW don't suggest changing it that's why its not done.
Check all electrics work, like windows, locks, sunroof.
Another thing if it's of any concern to you: some modern cars only give the airbags a 10 year lifespan before you're supposed to replace them. See if you can find the date sticker.
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