>>28522553
Cooling system? Check for leaks, lol. Bring a flash light. Check front suspension too, boots and struts are probably OE. Open all the doors, make sure all the power windows work, turn on the a/c to cold, then check the heat. Turn the radio on. Check how crappy the headliner and A pillars are. Remove floor mats and run hand under where each mat was, check for wet or dampness or signs of it.
Can't check without removing, but I bet both front and rear air intake boots are split on the bottom and you won't see this till you change the air filter. Check all rubber and hoses while in the engine bay. Start car, listen for ticks, bad pulleys or squeels, etc. Inspect belt and hoses before starting car. Open trunk, make sure tools are in the BMW tool box. Inspect weatherstripping. Open glove box, make sure BMW flash light still there. Go for test drive, get it up to temp, get on the freeway, open it up a bit. Check for vibrations, and at what speed or grinding from rear end. Brake hard, see if it pulls left or right or shakes. Go back, park, get flash light, go look under front of car under engine now that it's been driven, see how many oil leaks drop or coolant. That car has a dipstick, check the oil.