I have cleaned up my system using the recovery tools supplied with my computer. OS is an XP updated to SP 3. The recovered system included an install of Acrobat Reader 6.0. I tried to update to version 7.0 using the Readers own update-function. The installer/updater gave me this mysterious error right away when, I think, it was still unpacking files: "Error 1325.Documents is not a valid short file name."
The same happened when I tried to uninstall the same Reader 6.0. And it happened again as I was trying to install 8.0 manually and the same with installing the new 9.0.
I somehow got my hands on Acrobat cleanup utility, I ran it, but I was still not able to uninstall version 6.0. I ran also Windows' own registry cleanup utility, deleting all registries of Reader 6.0. That, probably, worked and Reader 6.0 was disappeared from the list of programs (Add/remove programs). Afterwards I was able to delete all visible files of Acrobat Reader 6.0: from Program Files, Common Files and Documents and Settings\Application data.
No sight of Acrobat Reader 6.0 on my computer but still the problem persists when trying to install newer versions, eg. Reader 9.0 reports the error just a second after the installer is launched.