Don't forget to update any Docker instances of OS's. My brother just challenged me and I'd assumed my Docker Ubuntu instances would be updated automatically by updating the main Ubuntu OS but that was not the case. In my defense I'm still new to Docker.
I also used this to list my containers:
docker ps -la -n=100
docker images
docker run -i -t ubuntu /bin/bash
env X="() { :;} ; echo busted" `which bash` -c "echo completed"
Edit: Updating the container then committing it (Docker terminology) should ensure that container stays updated, though any new runs creating new containers would continue to be vulnerable I suspect until Docker patches them or whomever would be responsible to do so.