Basic Pointers from my end
Ensure to check the exterior of the vehicle in bright sun light. Avoid evening time as you may find it difficult to see the difference in paint else you shall have paint thickness check pen.
When you turn on the engine check for any abnormal noises. Better to open bonnet to ensure no oil leaks.
When you go for a test drive ensure to keep all window open to check for any noise during drive.
Better to take a test drive on unpaved road to check suspension and jerks if any.
Try reverse gear too just to check.
Apply brakes and check if the vehicle deviate from its actual path.
Inspect tires manually. Follow coin rule or even check with your finger for the tire thread. ensure tires are not very old.
Check all electronics like all windows, lights, wipers, sunroof mechanism, if its open roof, check for roof mechanism.
Ensure that vehicle is GCC specs.
Check for service history and recent repairs.
Check for cleanliness of interiors.