I recently upgraded a Mint 13 Cinnamon 32 bit to Cinnamon desktop 1.6.
The easiset way for me was to log out of Cinnamon. Log in to Gnome 3 Classic.
Change the software sources: + romeo.
Then all the Cinnamon 1.6 desktop upgrade and packages appear as 1 proirity update in the update manager.
Update the system.
Then log out of Gnome 3 classic, and log back into Cinnamon 1.6 with zero problems.
Change the software sources: - romeo.
When I tried to do this while logged in to the Mint 13 Cinnamon desktop it got ugly for me:
no title bars! no scrollbars! no bottom panel! no start menu.....
I searched and found this post:viewtopic.php?f=47&t=113830
And of course, zz was right:
gir1.2-muffin-3.0 was not installed (when I had been logged into the cinnamon desktop while trying to upgrade it)
Edited for punctuation.