There seem to be some missing dependencies in docker.io package. Here are the steps to get docker running in Linux Mint 17.2:
apt-get install apparmor lxc cgroup-lite
echo "deb https://apt.dockerproject.org/repo ubuntu-trusty main" > /etc/apt/sources.list.d/docker.list
apt-get install docker.io
If you want to use docker as simple user you have to add this user to the docker group. Don’t forget to relogin if you add your actual user to a new group.