Do you know any application which would give me a more user friendly feedback (e.g. "faulty memory in bank 2")?
The problem here is that there isn't any reason why the application would actually know which SIMM a particular range of addresses maps to. The phsyical layout of memory (that is, which chips on which SIMMs) is for the most part controlled by the memory controller in the system.
Try moving the SIMMs around and see if the address ranges with the largest distribution of errors moves with it. This might give you some idea which SIMM is faulty.
It might be that simply cleaning the connector pads and reseating the memory fixes the issue even. A dull contact is not good when you are dealing with signals that are switching millions of times a second.