My advice would be to check the bodywork as Mini's do not wear the miles partically well. So look for chips on the bumper, bonnet and windscreen plus corrosion/discolouring on the lower and upper chrome grill.
Also check the alloys for corrosion under the lacquer. Do not assume as its a young car there will be no wear.
I found the battery was not even seated in its tray properly on mine and it was from a Cherished mini dealer, so check without breaking the flimsy plastic cover.
Check even tyre wear too with plenty of tread as these are run flats £££.
Check next service due along with TLC if it has one. Worth buying TLC XL if you plan to keep.
Apart from that just make sure all the electrics work, like stop/start, keys, washers etc.
Good luck and if it not perfect, walk away. Plenty more out there...
If they do not come down on the price then get some xtras thrown in if from BMW. I got stripes, iPod lead and Colour line rooster.