Error while updating.

The PPA doesn't support Precise as you can see with:
http://ppa.launchpad.net/kubuntu-ppa/backports/ubuntu/dists/

You should remove the PPA

how can I remove it?

Use software sources in dash or run:

sudo apt-get install ppa-purge
sudo ppa-purge ppa:kubuntu-ppa/backports

skydos@skydos-Satellite-L300:~$ sudo apt-get install ppa-purge
[sudo] password for skydos:
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following packages were automatically installed and are no longer required:
  python-mako gir1.2-gst-plugins-base-0.10 libdiscid0 gir1.2-ubuntuoneui-3.0
  rhythmbox-data libdmapsharing-3.0-2 python-markupsafe librhythmbox-core5
  gir1.2-rb-3.0 libmusicbrainz3-6
Use 'apt-get autoremove' to remove them.
The following NEW packages will be installed:
  ppa-purge
0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded.
Need to get 4,360 B of archives.
After this operation, 57.3 kB of additional disk space will be used.
Get:1 http://archive.ubuntu.com/ubuntu/ precise/universe ppa-purge all 0.2.8+bzr56 [4,360 B]
Fetched 4,360 B in 1s (2,848 B/s)
Selecting previously unselected package ppa-purge.
(Reading database ... 427081 files and directories currently installed.)
Unpacking ppa-purge (from .../ppa-purge_0.2.8+bzr56_all.deb) ...
Processing triggers for man-db ...
Setting up ppa-purge (0.2.8+bzr56) ...

skydos@skydos-Satellite-L300:~$ sudo ppa-purge ppa:kubuntu-ppa/backports
Updating packages lists
W: Failed to fetch http://ppa.launchpad.net/kubuntu-ppa/backports/ubuntu/dists/precise/main/source/Sources 404 Not Found

W: Failed to fetch http://ppa.launchpad.net/kubuntu-ppa/backports/ubuntu/dists/precise/main/binary-i386/Packages 404 Not Found

E: Some index files failed to download. They have been ignored, or old ones used instead.
Warning: apt-get update failed for some reason
PPA to be removed: kubuntu-ppa backports
Warning: Could not find package list for PPA: kubuntu-ppa backports

ok lets do it manually, what is the output of:

grep -R kubuntu-ppa /etc/apt

Thanks

skydos@skydos-Satellite-L300:~$ grep -R kubuntu-ppa /etc/apt
/etc/apt/sources.list.d/kubuntu-ppa-backports-precise.list.save:deb http://ppa.launchpad.net/kubuntu-ppa/backports/ubuntu precise main
/etc/apt/sources.list.d/kubuntu-ppa-backports-precise.list.save:deb-src http://ppa.launchpad.net/kubuntu-ppa/backports/ubuntu precise main
/etc/apt/sources.list.d/kubuntu-ppa-backports-precise.list:deb http://ppa.launchpad.net/kubuntu-ppa/backports/ubuntu precise main
/etc/apt/sources.list.d/kubuntu-ppa-backports-precise.list:deb-src http://ppa.launchpad.net/kubuntu-ppa/backports/ubuntu precise main
grep: /etc/apt/trustdb.gpg: Permission denied

Oh God...

Thank you actionparsnip... this solved my problem.

Thanks actionparsnip, that solved my question.

Today, I experienced exactly the same problem. I did manage to remove both ppa's from the software sources in Muon, the graphical software manager in Kubuntu 12.04. However, one question remains: when will it be possible again to add a ppa/ppa and ppa/backports to the software sources?

PS. Also when trying to add both ppa's via a graphical package manager, I experience exactly the same problem.
Also in that case, the only option is removing both of them from the software sources.