The odd thing is, that if I want to show "mach f", the fourth multiplex phase isn't shown. But if I put "macqxx" in the buffer, it does work. Clearly there's something wrong with my looping conditions, and it is influenced by the characters to be displayed. But if I simulate it all in MPLAB, it does go OK.
Maybe, just maybe, it has something to do with the fact that I set the target architecture in MPLAB (the Microchip assembly IDE) to 16F628, while I'm working with the 16F628A -- version 5.7 of MPLAB IDE doesn't have the 16F628A yet. I'm downloading the newest version right now, see whether that helps.
It gets curiouser and curiouser...
EDIT: No, that wasn't the solution. More debugging tonight!