My 320 is in having this sorted as I post this. Apparently its common that the filter on the washer pump gets blocked if you use standard (cheap) screenwash fluid.
The solution is to strip the system and clean or replace the filter. Then use original BMW or similar high grade screenwash concentrate in the future.
Apparently, its a common problem and is to do with the viscosity of some fluids. The mechanic suggested the fluid needs to be methanol-based (not sure whether he means methanol-free). VWs and Audis can also suffer the same problem.
Jimbo
December 2008