There are a number of possibilities here. The circuitry involved consists of the processor, which provides the memory controllers, the board, which provides the support circuitry for the memory buses (termination resistors, etc.) and the DIMMs themselves, which provides bus interface circuitry and the DRAM I/Cs themselves.
If you are saying that the errors stay with the DIMM slots, even when you swap the positions of the individual DIMMs, then you are looking at a failure on the board or in the processor. The processor is the easiest thing to swap to see if this isolates the problem...
Hope this helps,