Oh well, the upgrade seemed fine - although I chose the graphical upgrade because I'm quite busy here at work and I didn't want to follow too many instructions about editing files and so on. After the required reboot, it just went bad. I couldn't start my Mint. After having miserably abandoned my Mint in that state, yesterday I decided it was time to do something about it so I entered the recovery mode. I started with fsck just to be sure everything is right on the HDD before anything else. One of the bottom options are starting the network and going to the console. I chose that option and the network started, but when Mint asked me for the password I typed Ctrl-D to exit the console and continue with the rescue session. After that, I chose Fix broken packages from the rescue menu. Mint went checking up everything on the internet, offered to uninstall almost everything and install back. As I had nothing valuable to lose, I went for it. About half an hour later I restarted the system and it was OK. You will only have to answer some questions after the configuration of the packages starts.
If you have important data it's safer for you to backup everything. Normally nothing can go wrong with your data but just in case anything happens at least you have this advice. The packages reinstallation was a success - I am typing this messenge from my upgraded Mint "Gloria".
Good luck!
