Overall the 1996 to 2001 A4 was quite reliable. That said it was plagued with a variety of recalls. The first affected only 1,997 1996 through 1997 vehicles (as well as the 1995 90 series). A discharge of static electricity could ignite the driver's side when entering or exiting the vehicle causing airbag deployment. A simple ground wire was the fix.
The second recall affected 2,767 1996 to 1997 vehicles, each of which had a plastic ignition switch housing that could fracture at the return spring anchor point, causing the return spring force to be insufficient for returning the ignition key to the running position after starting the engine. The result would be inoperative electrical accessories such as windshield wipers and headlights. The obvious fix was replacement of the ignition switch with a modified switch.
The third recall affected 9,000 1997 through 1999 models that had a faulty control valve in the vacuum hose connecting the brake booster to the intake manifold that might not open or close fully at temperatures below -4 degrees F, potentially causing a loss of power brake assist. A vacuum by-pass system was installed on affected vehicles.
1998 recalls included 1,437 cars affected by an air screen that was loosely seated in the air flow meter that could become dislodged in the case of a backfire and block the throttle plate from returning to its full idle position. A screen retaining ring was installed.
The fifth recall involved 4,900 1998 and 1999 cars affecting the steering assembly tie rod seals that didn't seal properly. If moisture and/or dust particles entered the swivel bearing mechanism, the swivel bearing may wear over time to a point where the steering begins to feel 'loose' and could diminish the steering control of the vehicle with the potential to lose control. The fix was to replace the tie rods. It seemed that by the time the 2000 and 2001 models came out they'd got it right as there were no more recalls.