I have a server running 12.04.4 32 bits Ubuntu server, and I wonder if there could be any unsolvable problem updating to 14.04.1 as the terminal suggest me (using do-release-upgrade) to do.
I just upgraded from 12.04
If you really want to be certain. Install 14.04 in a virtualbox and then install all the normal software you use to try it out first.
Here're the problems I had when upgrading...
One annoying problem is the "diskfilter writes are not supported" message, it can brick a remote server. But it may not affect you if you don't use LVM/raid. You'll need to plug in a monitor and keyboard and press enter to continue... Diskfilter writes are not supported > What triggers this error?
All the files in /etc/apache2/sites-enabled need to end in .conf now. And there're various apache 2.2 to 2.4 changes. Options now need a + sign, and changing allow/deny to require in all the configs. http://httpd.apache.org/docs/2.4/upgrading.html
With any upgrade, manually installed programs/modules may need to be recompiled. And if you're using an old project that hasn't been updated for a while it may not compile. Best to test that first.
I wonder if there could be any unsolvable problem updating to 14.04.1
It is impossible for us to answer your question with "yes". In general it will work but your system might have all kinds of tweaks and changes that can interfere with your upgrade.
Mind you: if your files are important to you you already make a regular backup and also reguraly check if you can restore that backup. So if anything goes wrong you can re-install and restore that backup.