I got this check list from a fren , the main thing to check when receiving a new car...
Check all the buttons on your remote works.
Visual inspection of the car's body to check for dents and scratches.
Check chassis number.
Visual inspect the engine for any leak or overflow. Listen to the engine sound for any abnormality. (example out of tune, trembling, low idle). Give it a few rev and hear the exhaust for any loose metal particle.
Browse through the Info on the lcd on the dash to make sure its working properly. Also check the gear position to see if it matches.
Check undercarriage for any signs of damage.
Check all windows at the front, all doors and back for any abnormalities.
Check alarm system-by key or manual
Check the lights, wipers, horn, aircond, interior lighting, power windows and child lock to make sure all in working order. Don't forget the cigarette lighter.
Bring some CDs to test the ICE and check if the CD changer is working properly.
Check the A pillar and radio head unit is fixed properly.
Check the front chairs movable front back and up down for drivers chair.
Check the rubber/floor mats are in place or missing.
Check the leather seats for discoloration and bad stitchings.
Check the rims as best you can for dents.
Check the tyres are fitted in the correct orientation.
Check the boot area fittings and the spare tyre + tools.
Check the back seats 60/40 fold is working properly