Shutter seems to be missing some perl dependencies in repositories to have the edit feature installed by default. You can add packages by hand (they work fine) with:
{CODE(colors="shell" ln="1" caption="Commands in a terminal")}
cd ~/tmp
wget https://launchpad.net/ubuntu/+archive/primary/+files/libgoocanvas-common_1.0.0-1_all.deb
wget https://launchpad.net/ubuntu/+archive/primary/+files/libgoocanvas3_1.0.0-1_amd64.deb
sudo dpkg -i libgoocanvas-common_1.0.0-1_all.deb
sudo dpkg -i libgoocanvas3_1.0.0-1_amd64.deb
wget https://launchpad.net/ubuntu/+archive/primary/+files/libgoo-canvas-perl_0.06-2ubuntu3_amd64.deb
sudo dpkg -i libgoo-canvas-perl_0.06-2ubuntu3_amd64.deb
sudo apt-get install -y libextutils-depends-perl libextutils-pkgconfig-perl
sudo dpkg -i libgoo-canvas-perl_0.06-2ubuntu3_amd64.deb
sudo apt-get -f install
{CODE}
Then close shutter, and shutter indicator icon in the task bar, and restart it again. YOu'll be able to edit images again from within shutter.