Firefox was closed, then I tried to open it via clicking the *.desktop file.
When Firefox is already open, then I think it was the same error response.

I found https://bugs.kde.org/show_bug.cgi?id=283475 which looks like the same issue. I'm not sure if I understand their solution but it seems that the issue is resolved with KDE 4.11. Which takes me back to what freininghaus wrote earlier: KDE 4.8.5 is outdated. So my questions are:

• How do I update Kubuntu 12.4 LTS to KED 4.11?
• In case of problems, is there a way back to KDE 4.8.5?
• Does KDE 4.11 comply with 12.04 LTS? (since for some reason, KDE 4.8.5 is still distributed with 12.4)

Right, I completely forgot about that bug - probably because it was fixed so long ago

I don't know if you can upgrade Kubuntu 12.4 LTS to KDE SC 4.11 or later, you would have to ask the Kubuntu people about that. However, I think that the target audience of these LTS releases are users who prefer to have a system that does not change much, and who are willing to pay the price for that (i.e., use extremely outdated software). Therefore, the only way to get a more recent KDE might be to update the entire distro, but I'm not sure.

I would suggest asking on the Kubuntu forums - if I recall correctly there is a PPA (at least for the latest released versions of Kubuntu) which provides the latest version of KDE (currently 4.12.2 I believe).

I asked my question there, and here https://www.kubuntuforums.net/showthread.php?p=346828 is their answer, just in case someone has the same issue.
Basically, they recommend upgrading to KDE 4.12, tell how it is done and also about possible risks.

Thank you all very much for your kind help.

Edit: I upgraded to KDE 4.12, problem solved .