Can I mix sources from different ubuntu versions?
Solution 1:
12.10 is already beyond end of life.
But to answer your question, in general, unless you have a great deal of experience with apt, it is a bad idea to mix repositories. In your case, the packages in 12.04 are almost certainly going to be older then the packages in 12.10, and so it will do you no good.
In theory you can mix repositories using pinning, see https://help.ubuntu.com/community/PinningHowto
However, when pinning one generally installs a few packages.
In your situation, rather then mixing repositories, you would upgrade.
Because 13.04 is also at EOL I suggest a fresh install of 14.04. If you do not format your root partition, your data in /home
will be preserved.