Docky needs a composited desktop to run and display correctly. In Gnome, either enable Compiz by going to Menu=>Preferences=>Appearance=>Visual Effects and checking "Normal" or higher, or gor to Menu=>Preferences=>Desktop Settings and, in Windows=>Performance, check "Use Gnome Compositing"
You may also find that you get the same black outline for a few seconds when you boot Mint. Or, you could get a notification box saying that Docky requires desktop compositing to work properly. If this is too annoying, you will need to put in a delay before Docky starts.
Open Gedit and type "sleep 10 && docky" ( without the quotes). Save this to your /home folder in a file labeled ".dockysh" (again, no quotes). Right click the file and open Properties. In the Permissions section, make sure the box for "Allow executing the file as a program" is checked
Open Startup Applications (Menu=.Preferences=>Startup Applications), find the entry for Docky, click it to select it, click Edit, and change the command to read "/home/your username
Now, when you boot into Mint, the desktop compositor will have time to start before Docky starts so you have no black outline at startup.