things i'd check for when buying a used car:
Visual inspections:
1. Check around gasket areas to see if there's any oil leaks
2. Pull up the oil dipstick and see the condition of the oil. If it looks milky color, then there's probably a blown head gasket, if the oil is brand new either the owner keeps his car very maintained in which you should ask for maintanance records or there's something going on with the engine.
3. Check all fluid levels to see if they are maintained (brake, power sterring, transmission, oil, coolant, windshield,)
4. Check the condition of the coolant - is it green? is it brown?
5. Check the tires for uneven wear - usually indicates misalignment or some other bigger problem.
6. Check the sides of the area around the front and see if vehicle was repainted.
7. Ask for proof of when the last major maintanance occured (timing belt change, spark plugs change, valve job perhaps, clutch if its manual, etc etc)
After that, start up the car yourself, and see how the engine responds and drive it around a bit.. remember that an engine is still good if you can feel it "pull" you and not "push". While driving the car, check:
1. Gear shifting - is it smooth or does it jump
2. Smooth acceleration or uneven acceleration
3. shocks/springs and brakes - does it brake smoothly, does the car respond well over bumps
hopes tis helps - and remember to use common sense, if you THINK something's wrong with the car, then your probably right.