its a long list,
so I'll try to write briefly
- check the idle from cold and from hot, it musnt fluctuate
when hot must be between 550-650 rpm range if AC is not on..(a high fluctuating rpm means leak or dirty icv or other problems)
also an irregular shaking engine says there is a problem..
- check the plug wells for oil
- check the coolant in reservoir for unusual color, bubbles,and other unexpected things
- check the oil
- check engine noise for unusual misfires, or unusual noise from bearings and also when AC is on
- from cold check the radiator coolant pipe on the passenger side for heating slowly if yes thermostat gone..
- check the fans are kicking at expected temperatures and when AC is on..
- from underneath the car,check for oil and coolant leaks..if yes , repair will be necessary..
- check for unusual exhaust noises, rattles, leaks and corrosion..miggy exhaust system is not cheap
-if possible use a lift and with a lever check engine mounts, steering arms and other components for play..
-check wishbone bushes for leaks and excessive play..
-check brake disc surface and thickness and pads..
-check tire gaps on the front and rear to bumper are equal (measure it)
- check the conditions on the tires, if they wear uneven there may be geometry problems
- when engine working measure the volts of re-charge..
- check the AC system is cooling adequate..
- check the sunroof tilt up, or completely open
-check the road computer for dead pixels
-check the ignition key can turn freely
-check the smell inside the car when the heater is on ,
if smells sweet coolant, check the driver side carpet
for any coolant leaks-traces..
-lock-unlock the doors with remote
-check if you see any engine management light is on when the car is working
-check all lights internal-external..
check the door gaps are equal , bonnet and other parts are symmetrical
-check for stone chips on the bumper if you dont see any its painted..
-check for unmatching color tones on all parts..if yes its painted..
-if the wear on the steering, gear knob or chairs are excessive and the car is relatively low on mileage they played with the cars mileage..
-and now drive the car for some time, try brakes, gearbox and listen to unsual noises and check for hesitation..
- and if possible ask for a compression test (if you can have it or not)
also there are many other parts that needs checking but thats all I can remember for now :-/