Dynamic resizing of screen doesn't work in Parallels
Solution 1:
The version of Parallels Tools that comes with Parallels 7 doesn't support Ubuntu 12.10, but it's possible to install the version that comes with Parallels 8.
If you download the trial version of Parallels Desktop 8 and mount the disk image, you'll find the Parallels Tools ISO at /Volumes/Parallels Desktop 8/Parallels Desktop.app/Contents/Resources/Tools/prl-tools-lin.iso
. Mount this ISO in your Ubuntu VM and follow the usual instructions to install/upgrade the tools.
("Parallels Desktop.app" is flagged as hidden and doesn't appear in Finder, but you can still copy the ISO out of the disk image using terminal.)
I did this with my Ubuntu 12.10 VM on Parallels 7 and dynamic screen resizing works fine.