Is the owner's manual missing?
Any maintenance records for the vehicle? Are there large gaps in the service history?
Do you suspect the mileage isn't legitimate? Does the title include the word salvage?
Where has the car been serviced? Why do they want to sell the car?
Any accidents, engine, transmission repair?
Any oil, coolant or fuel leaks from the engine? Is there oil on the engine?
Is the oil level low?
Is the oil on the dipstick too black? Any evidence of badly made repairs?
Does it sound rough?
Any knocking, pinging, and whistling? Any smoke?
Any warning lights go on while the engine is running? Is the engine oil pressure too low at idle?
Any acceleration delay after heating up?
Is there sustained visible smoke coming from the exhaust?
Does the transmission fluid smell burnt? Is the fluid on the dipstick too dirty?
Start the engine and switch from Park to Drive and from Park to Reverse while holding the brakes. Any problems?
Is the time between switching the lever and the transmission being engaged too long?
Any noises or jerks during shifting?
Any leaks?
Any noises while shifting gears? Any trouble shifting gears?
Does the transmission jump out of gear? Is the clutch slipping?
Is there play in the clutch (very loose)?
Any leaks from the clutch master - or slave cylinder?
Any delays, clunks, or other troubles when the transmission is changing gears? Does the transmission slip?
Is any gear/speed missing (i.e. shifts from 1st to 3rd, reverse doesn't work)?
Is any gear/speed stuck?
Any shifting problems when the engine is cold?
Are the body lines straight?
Are the gaps between body panels uneven along their length? Has the car been repainted?
Are there mismatched colors or different shades?
Is there painting over, spray, or any traces of body repair?
Are the doors, hood, or trunk fastenings readjusted from their original position? Are trim pieces missing?
Are the shock absorbers oily? Are the shock boots torn?
Is there too much "free play" in the steering? Do the tires have irregular wear?
Do you detect any movement in the tie rods and suspension mounts? Is there any bent or dented metal along frame mounts?
Jack the vehicle up and support it safely. Tug and push on the wheels. Is there any lateral play?
Any knocking noises coming out of the suspension?
Does the vehicle pull to one side while driving?
Is the brake fluid reservoir oily or sweaty on the outside?
Is the brake fluid level too low?
Is there too much "free play" in the brake pedal?
Any brake fluid leaks under the vehicle?
Are the brake lines weather cracked or not secured properly?
Brake firmly. Does the brake pedal feel soft or mushy?
Does the vehicle veer to one side while braking?
Do any of the wheels not brake properly?
Do you feel any vibrations or noises while stopping the vehicle?
Does the brake or antilock warning light come on while braking?
Are there tears or worn areas on the seats? Are the seatbelts working properly?
Are there cracks, blemishes or broken trim? Do the climate controls work?
Do the audio controls work? Are the locks working?
Are the windows working?
Do all power accessories work (i.e. wipers, power mirrors)? Are the spare tire, jack and tools damaged or missing?
If after completing this list the vehicle meets your standard of approval, you should take it to a certified vehicle technician/mechanic for a mechanical inspection. Try to choose a mechanic that specializes in the type of vehicle you are planning on purchasing. Remember you are paying them to find anything wrong with the vehicle. Do not use a mechanical inspection provided by the seller. If you are looking at a collector or special interest vehicle, you may want to consider an appraisal.
Source: YouTube
In this video, the presenter walks through some of the initial inspection steps he takes before contacting the seller to take a test drive.