Check all the pipes for any sign of perishing (especially at the ends). Also check for any signs of dampness on the pipes, as this would indicate a slight leak. It doesn't take much of a hole to let air in, and it may even be a porous pipe. To narrow down your search, buy a length of hose, and disconnect the hose going into the fuel filter. Connect one end of the new bit hose onto the filter, and put the other end in a container of diesel. Now run the engine, and see if any air is being drawn in (also try briefly blocking the end of the hose, to create a bit extra vacuum to see if any leaks are apparent). If there's no leaks, the problem lies further back in the system. Have you checked the connections on the fuel tank? Or if the pipes on the fuel tank are rusty (if they're steel)? It may also be a blocked pick-up filter in the tank.
I'm not entirely sure how much electronics were on the Audi 80s, but the air may be causing the ECU to think there's a fault somewhere. I'd ignore the fault until the air problem is sorted, as it may be a symtom, rather the cause.