Hi Pat,

As with all premium models in particular, be very strict on the service history - don't risk a car with none or a patchy history. 

Now, specific to the A4 of that era, watch out for:

 - The ESP light remaining on after the engine starts (means adjustment of the pedal position switch, so nothing major).

- Noisy heater fan or not working at all (might mean replacement necessary).

- A fault inside the auxiliary heater can cause widespread electrical issues including preventing engine starting and even the electronic parking brake from working.

- The alarm can go off randomly due to faulty keyless door handle sensors.

- The sunroof switch can fail.

- If the centre console lights or the auxiliary power socket are not working then it means the wiring harness is damaged.

- The headlining at the back can get damp due to blocked sunroof drain tubes (that can cause the satnav to stop working, too).

- The automatic transmission can be jerky and cause warning lights to come on (it might need to be reprogrammed).

- A fuel pipe in the 2.0-litre diesel model can rattle against the fuel tank.

Hope that is of use