Has it ever been stolen / recovered?
Has it ever been in a minor or major accident?
Can I see the receipt, service history and bills please?
Have you ever modified the vehicle in any way (suggest you need to inform your insurers if this is so)?
Check the mileage intervals between services (dates and miles to see what kind of usage the car has had - short service intervals indicate its used for company mileage)?
Has it been garaged during its life?
Why is he /she selling the car? (they can tell you anything they like, but their response can often guide you to an answer) - if they are upgrading it is likely there is nothing wrong with the car, if they are changing for an 09 plate then ditto. If they are changing like for like be more suspicious.
Has the car had any repetitive service related issues (if you suspect anything note the servicing dealer name and then phone them independently to say you are looking at buying this car, and do they hve any history of warranty work or expensive repairs they can share with you) - some may say this is a back handed approach, but if it is an expensive car then you need to protect yourself.
How much warranty is left on the vehicle?
How much tax is left on the vehicle?
When would the car be due an MOT (if appropriate)?
Then
- Check the shut-lines of the body panels of the car to make sure it all looks straight
- Check the VIN plate in the window (passenger side) matches the V5
- Pull back the carpets in the boot and check for irregular welding / overspray (paint), or anything that indicates a heavy rear impact
- Check the boot opens and closes correctly and that all the rear lights are working as you'd expect (take 2 people to confirm this)
- Check all the doors open and close smoothly and w/o sticking or effort to reclose
- Check the oil filler cap for white residue (potential head gasket or sign of lots of short journeys)
- Check the under bonnet condition - does it look right for a car of its age (too clean can be as much of a concern as too dirty if it is inconsisitent with the cleaning standards of the rest of the car)
- Turn on the car and make sure it: starts first time / there are no warning lights on the dash / that the idle sounds fairly consistent / blip the throttle lightly to make sure the idle returns to the normal level without excessive hesitation
- Check all the electrical switches work (inc. radio), switch a load of electrics on at once to see if the headlights dim excessively (sign of worn battery / alternator). If there is a trip computer make sure it works and that all the menus work. Read the fuel figures on the trip gauges as they will give you a sneaky peak as to how the car has been driven (if they haven't reset it)
- Put tyres on full lock and check for inconsistent wear across the tyre profiles
- Push down on each corner of the car to ensure the springs & dampers are working efficiently (if car bounces more than once before returning to position they could be on the way out - if so are there any leaks on the dampers)
- See if you can conduct a visual check of brake pads. If they aren't visible due to wheel type, run your finger across the brake disc to see if they are OK (not heavily ridged or warped) - ONLY DO THIS WHEN THE CAR IS COLD OR YOU'LL TAKE THE SKIN OFF YOUR FINGER TIP!!
- Get someone to check the exhaust round the back when the car is running in case of any (blue smoke / blowing / excess smoke)
- Take a magnet with you, and put it inside a microfibre cloth, then run it along any suspect panels for signs of filler - magnet wont stick obviously!!!
- Use one of the mobile phone checkers to ensure the info matches their descriptions (like this LINK)
Nothing else comes to mind at present, but others on here will know of current issues to check (maybe things like knocking wheel bearings on a test drive).