Yay, at last a worthy reason to register!
I'm running a similar setup to yours: Linux Mint 14, Cinnamon 1.6, AMD CPU, Radeon GPU; and the exact same problem has been plaguing me since Mint 13.
The only solution I found so far was to minimize calibre to the tray then restore it, ten times out of ten it results in a normal sized window. Running calibre in debug mode seems to have no effect on the issue, it still starts with the miniaturized interface.
Though, for me the problem only occurs if I close calibre and try to reopen it without rebooting. That is, the interface is normal the first time I start calibre.
I use the modern interface, have 1 plugin (Count pages) installed, and added 2 columns (Format, Words).
Screenshot with the debug log
Let me know if I can be of any help.