Martijn:
You need to remove one level of complexity from your test case. The scrolling may very well be totally confusing the issue!!

The best way to handle the mapping issue is to simply write all the bytes in the DDRAM in sequence with increasing byte values. I suggest that you start with initializing and clearing the screen. Then write a loop with 80 repetitions of data outputs to DDRAM starting with 0x21 then 0x22 0x23 and so forth. If this does not result in something showing in all character positions of the LCD then you know that you either have a faulty LCD or you did not initialize it properly.

You also need to note that not all LCD modules that are physically built as two lines of characters are initialized as "2-line display mode" in the FUNCTION SET command. There are plenty of small displays that need to be programmed into "1-line display mode". (This has to do with the geometry and layout of the electrodes on the LCD glass and pinning connections between the controller chip and those electrodes. Not all vendors connect things up the same way!!).

Michael Karas