..this cars are usually kept by people who are enthusiastic and by having double seater nature, these cars are most probably have not been exposed to some harsh usage, therefore, it should be fine..either way, this is what you should look at:
INTERIOR
Do all the controls, switches and displays work properly?
Take a music CD with you and check operation
Check the A/C works (an expensive repair)
Do all the lights work? Get someone to stand behind and check the brake lights.
Are the carpets and seats all dry? If not, is there a leak?
Does the wear on the interior reflect the mileage - high wear low mileage WALK AWAY?
If Sat Nav fitted check the maps are up-to-date
BODYWORK
Is the bodywork free from dents, scratches and rust?
Check panel fit on all panels for signs of accident repair
Make sure you are not checking the car in the wet or the dark, as you are more likely to miss problems
Squat down and look along the sides of the car to help you spot mild dents
Pull back rubber seals around windows. Is the paintwork free from over-spray and suspect repair signs?
Look for signs of additional layers of paint, or ill-matching spray marks where an additional layer of paint has been added but the finish is not right. These are signs of an accident repair
Open the boot and bonnet. Is the metal work in good condition? Wherever there is exposed metal you need to look for ill-matching colours or buckling. These are signs of an accident damage.
Try the roof – up and down smoothly
ENGINE / MECHANICALS
Is the exhaust smoke-free when the engine is warm? If not, there may be a problem
Is the coolant reservoir full of brightly coloured coolant? It should not be empty or brown. If not, are there any leaks that need further inspection?
Is there plenty of clean oil in the engine?
Take filler cap off and look for signs of emulsion (white/yellow gell) which may indicate head gasket problems – not a common issue on BMs but worth a quick check
Check service history and documentation
Note: BMW will help confim history if you provide reg. number and VIN
Check valid MOT – will assist in confirming mileage, if less than a year insist on a full year MOT (this at least will give you an up-to-date check on mechanical condition)
Check brakes/pads for wear (when were they last changed)
When was brake fluid last changed (every 2 years)?
Tyres – good tread left and all tyres match (are they quality tyres or cheap options)
Some Z4s have had coil spring failure – have any been replaced (if not they may need it in the future)
TEST DRIVE
Does the car drive in a straight line when you loosen your grip on the wheel?
Is the steering accurate and free from play or judder?
Does the car pull away and brake easily without any noises or judder?
Warning lights should all extinguish when car is started
Cruise control if fitted – does it work?
ACCESSORIES
If there are any get them thrown in for the price of the car - don't pay extra for them