Let's see. If you are going yourself, then check these things. This isn't a complete list, but has most of the common areas.

Engine:
Look for any unusual grease spots.
Listen for excessive valve tick.
Listen to motor at start up for any banging or anything unusual
Rev motor for any engine whine
Check under for any leaks
Open coolant tanks and see if coolant is blue and not green.

Tranny-

Test drive, check for 1 to 2nd hesitation, bucking, delays, etc
Check for 3rd to 4th hesitation, bucking, delays, etc
Listen to the tranny when the X downshifts from those gears.
Find any delay in R and D
Any lurching or Jerking

Suspension:
You are limited, but check with the owner in the car, place X in Drive and have him take his foot off the brake. After 10 seconds or so, have him jam the brakes. Watch carefully for the front wheels. Any movement within the well indicated some rubber component that is shot in the suspension. Looking at the picture, the guy has an incline drive. SO when you do test drive it, drive it up his driveway and listen for a clunk.

Exterior:
Check all lights.
Check for any body work. Now I can't remember what color it was, but I think black. If it is Black Sapphire, check carefully for any lightening of metallic flake. You will see the finish be nice in one area, but if you move your eye slowly, you can see spray over run from the metallic flake. Run your finger along all seams, checking for a step in paint.

Check all glass. Make sure they all have BMW logo. If not, ask what happened. If a replaced Windshield, usually it is because of a rock chip. If it is a side or rear window, either it was a break-in, accident, or Tiger Woods' Ex wife went Ape sh*t on it.

Interior:

Make sure all door handles work, inside and outside.
No Pixels out on Cluster.
No tamper dot by "Trip" counter
Excessive wear on seats, arm rests, etc.
Make sure all controls work.
Hard to test Rain Sensing wipers, just check outside if there is any bubbling around sensor.

Other Mechanical:

Check Air Ride suspension. Try to be there when you first start it. Any significant movement in ride hight indicates a problem with the Air bags. Use the control panel to raise and lower the suspension.
Check driveway for any oil spots and look under X carefully.

Well that is all I can think about now, good luck.

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2011 E70 50i M Sport