Here's something I wrote for a friend when they were considering buying an A3:
Most importantly run an HPI check on the car to see if it has any
outstanding finance.
You can also do a quick check on the registered model and number of
previous owners here:
http://www.rac.co.uk/web/vehiclechecks/dvla_lookup/
Interior:
Check all electrics, mirror adjusters, electric window switches, check
the aircon works (takes a while to get going) look at the MFA (press
the bottom of the switch on the end of the right hand stalk until you
see MPG Ø and that is average MPG).
Check the alarm, it may or may not beep when you press the lock button.
Check seat adjusters, there is little storage areas under the seats,
the passenger one should have the first aid kit in it.
All internal electrics sould work, check heated seats, air
conditioning (switch from lo to hi) and the readout on the dash should
have no lines running through it.
In the boot on the left hand side there is a handle, pull this and the
side comes away, behind this should be the Audi Sub in models with the
uprated stereo.
Underneath the boot carpet should be spare wheel and loads of tools
inside the wheel. In a recess at the closest to you side of the boot
should be a red box with warning triangle.
Check how many keys come with it, new they came with two remote keys,
and a thin plastic valet key. A new spare key from Audi is £150 so its
a good bartering tool.
Central locking should operate quickly with no delay after pressing
the button, and if you lock the doors with the button and keep it
pressed, the windows should close.
Newer cars will also have a cup holder mounted in the centre console.
Most audi's had a stereo which was a radio cassette, enhancements
included CD changer and Bose speakers. Sonata, Symphony and Concert
were the spec levels.
Seats and steering wheel should not show signs of excessive wear.
Exterior:
From 2000-2002 the cars underwent a facelift, changes included
removing the locks on door handles, headlight units, rear lights and
air conditioning unit.
Check for rust on the bottom of the doors, and also along the rain
guttering on the roof.
Check for deep scratches, dents and chips, these are expensive to fix
and hard to buff out as Audi paint is one of the hardest paint
compounds. On the plus side, light scratches buff out very easily.
Ensure all the lights work, and do not flicker, its common for one or
two LED's in the rear high level brake light to not work.
Check the rear wiper and wash, these often rust and cost about £70 to replace.
Engine:
All Audis usually have a full service history up to at least 100K Miles.
If mileage is 60-80K check the cambelt has been changed, this is a
must as its a £600 job. If the cambelt has been changed, the water
pump should have been changed at the same point, preferably with one
with a metal impellor. If the cambelt hasn't been changed, walk away.
When switching on the engine from cold there should be no blue or
white smoke and the car should idle normally.
Check the idle, it should hover around 900-1000rpm.
Check receipts for suspension, this generally needs replacing, ideally
after 70-90K miles.
No oil should be visible on the engine block, and oil levels on the
dipstick should be within the standard marks.
When turning on full lock and turning slowly, there shouldn't be any
creaks or groans.
Check the rear axle bushes, and the front wisbones and bushes for
wear, also take careful note of the Anti roll bar and bushings, this
tends to become worn and then rust.
Check brake pads and discs, the discs should not have a lip around the
edge as this indicates excessive wear.
Coolant should be pink and be on the max mark.
Oil filter should be clearly visible and black or bright orange, check
brand on oil filter if not a standard colour, this could be indicitive
of poor servincing and may mean correct oil was not used. (Oil should
be fully synthetic regardless of age, 0-30 or 5-40W)
After a 5 minute normal test drive getting used to it, drive it
quickly and brake hard and check everything stays in place, nothing
smokes and the coolant and oil temps stay in normal.
Other than the above, normal new car buying things should be taken
into consideration, like is the V5 registered in their name, is the
car clean and well maintained, how many previous owners etc, why is
the person selling, how long have they had it.