Welcome!
Check the MOT history for the car online for free, it should give you all the mileages and work that was advised, you can check if the work looks like it was carried out if anything major was listed recently.
Check if the service history matches these mileages. Check if they've installed bad or cheap or non-matching tires as this might indicate how they've looked after the car.
Apart from the general things you'd look at every car, you should pay attention to:
Lights on dash
- Check that all the usual suspects light up that when you first turn the key to position 2, and that they go out after starting the car. Sometimes bulbs are taken out to hide things so you will need to check if the light came on in the first place.
Mechanical
- Engine sounding - Any VVT Rattle or unexpected noises
- Easy to start or struggles etc.
- Can you feel the car making power normally or does it feel like the power delivery isn't normal
- Any leaks under the engine & gearbox (are they wet or dry)
- Gear engagement - Does it crunch, feel notchy entering gears? Do all the gears work fine?
- Is the clutch pedal too high?
- Does it slip in higher RPMS in 3rd gear onwards
- Do the turbo gaskets sound like they are leaking (common)
- Fuel pump noisy?
- Check the oil level on the dipstick to see if the oil looks clean and the level has been maintained
- If engine is cold, check the radiator coolant level and colour of the coolant, check for any strange substances.
- Any smoke from exhaust? Observe on idle, reving and during load during test drive
- Do you feel any knock from the diff or gearbox when you are lifting the clutch up
- Ticking noise when driving slowly when at full lock
- Sticky handbrake
- Idling okay?
- Doesn't overheat after idling for a long time, and can hear if cooling fans come on as usual.
- When car is hot, turn it off and see if it restarts easily
Body
- Rust on seams behind bumpers, where the chassis panels are bonded together.
- Heavy rust on the sils or wheel arches, tap on the bottom of the rear wheel arches with your knuckles to see if they are solid or falling apart
- Rust on the strut towers in the engine bay
- Rust where the spare wheel is
- Rust where the drivers pedals are
- Rust from inside where the fuel filler neck is
- Excessive Rust on subframes, especially rear subframe at mounting location
- If mudgards are still installed, check for heavy rust around them
- Gaps between panels, such as wings to door, door to quarter, boot to quarter, bonnet to wings etc.
- Check if any interior is damp such as carpets and seats, check boot as well.
Suspension
- Knocking sound when turning the steering left to right
- Knocks over bumps
- is the car excessively bouncy (damper may have failed)
- Put steering wheel straight and check the gaps between tires to body panels, they should match
- Steering rack or pump not leaking fluid
If anyone has anything else to add, please do so