Rust:
Check for rust starting from the engine bay, then do a thorough inspection of the exterior, then in the interior - lift up the carpet from the driver and passenger floors, check the door sills and finally on the sides of the carpet in the boot. These are common areas that an unmaintaned car bears rust marks.
Avoid rusted car at all costs, it's very difficult to get it under control.
Frame:
Either get under the car or have it lifted up at a service station. Check for serious dents in the underbody, then follow the frame and look for possible signs of dents, bends and welding points. If you find any, abandon the car. You will not be able to stabilize it.
Engine:
Try to call ahead and let the seller know you wish to test the car from cold start. The engine needs to be cold when you go to inspect the car. Open the engine bay, you can touch the top of the engine (valve cover) to see if the engine is hot or not. (Do not touch any pipes or the exhaust manifold - if the engine was previously running, you'll burn your hand).
Turn the key to ON position, do not crank yet. Make sure the necessary dashboard indicators light up - battery, heatup, oil, and most importantly the check engine light. Make sure you recognize these symbols beforehand (google them).
In some cars like Hondas, the check engine light shows up for a few seconds and goes off. In other cars, like Toyotas, the check engine light stays on. If the check engine light does not light up - that's worrying - sometimes when there's a fault with the engine and there's a fault code which triggers the check engine light, fraudia sellers remove the bulb from the check engine indicator to hide the issue. Turning the key to ON is how to check if the bulb is active or not.
Some cars have other indicators such as ABS, Airbag, etc.
Attempt to start the car when cold, see how long it takes to start up. It should take max 3 seconds. Any longer and it's a little worrying.
Go to the back and see if there's black smoke exiting the exhaust. That could indicate oil leakage or an engine running rich. Try to get close to the exhaust and if your eyes start to burn a little, that's an indicator of excess petrol - meaning running rich. Please don't place your eyeballs in the exhaust. Keep a little distance. White smoke during summer, or too much white smoke during winter could indicate coolant leaking into the block.
Once the engine is started, here are things to look for:
- Less than 2 minutes after starting the engine, open the radiator cap and check the coolant / water level. It should be full, and ideally should be coolant, rather than water. Presence of water indicates the driver does not care about the car, or coolant is leaking and they don't want to keep refilling coolant.
- Does the radiator fan turn on when car is started on cold? If yes, the fan is not auto and could indicate a cooling system fault. They will try to convince you how that's a good thing because maybe it's summer and too hot, it's all BS. Fan needs to be auto so your oil can run at optimal temperature. Your engine running on cool oil is not good for the engine.
- Check the RPM - on cold start, it should idle around 1200. Low RPM indicates faulty idle sensor or throttle body issues. High RPM could indicate someone trying to hide a fault.
- Does the engine vibrate? It could indicate bad mounts, or misfiring engine.
- Do you hear any some sort of tapping noise as you press down on the gas pedal? That could indicate a bad crankshaft - the engine is nearing death.
- Does the engine RPM increase smoothly as you press down on the gas pedal? If not, it's likely misfiring. Don't go above 4,000 RPM.
Gotta run, I hope someone else can pitch in on checking other systems such a suspension components, brakes, alignments, tyres, etc.
