A used car is a used car, so a good thorough used car inspection should eliminate any used car you don’t want to own. This inspection should include checking for bad paint/body work, modifications, abuse, neglect, etc., as well as verification that all systems work: lights, heater, A/C, all power accessories, door locks, etc..
First on the check list is to see if the car has properly sized/rated matching tires on all 4 wheels. Check for a spare and tire change equipment. If the car passes your basic used car inspection, then take the car for a test ride as a passenger and test drive covering the street and freeway (15 miles min).
As a passenger focus on how the car sounds, feels, how it runs through the gears, acceleration performance, and braking. Pay attention during this phase of your inspection. Keep the radio off and listen to the cabin and engine noises.
The test ride starts out with a cold engine start and while the engine is idling and warming up — A/C off at this time — listen to the engine for any ticks, knocks or other noises. As the engine warms up the idle should smooth out and slow down.
Go for the test ride. Once the engine is up to temperature have the driver run the engine up through a couple of gears, say starting out in 2nd at around 1K and running up to redline then shifting to 3rd and continuing to accelerate observing the posted speed limit or as driving conditions allow. If the car is an automatic, check operation in all manually selected gears and reverse, and the automatic shifting under normal and hard acceleration is smooth. What you want to know is that the engine pulls cleanly, strongly, from just off idle to red line.
After driving several miles the engine/drivetrain should be up to normal operating temperature. Continue to let the engine idle and listen again for any unusual sounds/noises.
Switch with the driver and take the car out over the same route and accelerate, stop, start, turn, etc. nothing too harsh. You’ll want to safely and within the confines of the traffic laws exercise the car and determine if the car feels solid and performs to your expectations for this type of vehicle.
Driving several miles and bringing the car to operating temperature will allow the engine computer systems a reasonable chance of detecting any problems and turning on the check engine light. When you start the car verify the Check Engine Light comes on then goes off at or shortly after the engine starts. This is normal in all in-dash warning lights.
Finally, if you can find no reason not to buy the car and believe you can buy the car for a fair price, arrange to have a pre-purchase inspection (PPI) at a shop by a technician familiar with servicing this type of car inside and out.
Do your research and determine the history of the car model you are considering. As a general rule avoid the 1st year of model introduction. Later model years generally have all the kinks worked out. Ask for all the service records, review the CarFax and check if the car was subject to a recall at http://www.recalls.gov/nhtsa.html.
After purchase if tire wear indicates uneven wear get a 4 wheel alignment. If no service records are available check the maintenance schedule in the owner’s manual and perform all required maintenance so you have a starting point for your own maintenance schedule as the new owner. This may include brake fluid flush, filter(s) inspection/change, coolant inspection/flush, transmission/differential fluid inspection/change, spark plug inspection/change, drive belts, and timing belt inspection/change. If you had the car go through a PPI some of the items may have been identified by your auto technician.