Open the bonnet and check that the dipstick indicates a good oil level and that the oil isn't black and sludgy. If it is an automatic, also check the transmission dipstick under the bonnet. While under the bonnet, also check that the radiator cooling fins are not corroded or missing. Listen for solid noises like rumbling, clattering and knocking. Warm the engine and leave the car in neutral.
Black smoke is also bad news, indicating excessive fuel usage.
While driving the car, check when braking that there is not excessive pedal travel, or pulling to the left or right. Proving odometer tampering If you think your car's odometer has been wound back, proving it is not as simple as you might think. Check the original window notice. If so, the law says that you have been warned before you bought the car and there is not much you can do. This is not adequate under the Motor Vehicle Dealers Act - it must be the exact warning shown in the above paragraph.