Denial of Service attacks are probably more straightforward than in a virtualized environment; I'm sure you could find a way to starve the kernel for something.
That said, there's currently no trivial "now I'm root on the host box" option or anything.
Please stop repeating this. Docker is not a security tool, apparently by their own decision. It hurts people to have that be part of the common knowledge.
And as another commenter pointed out, you can't give a user permission to actually start a docker container without also giving them root access to the host.
[1] https://docs.docker.com/articles/security/ [2] http://lwn.net/Articles/626665/
For me it's about creating a setup that is far more easy to reproduce in the face of e.g. system upgrades, setting up a new machine, as well as protection against stupid mistakes, and about containing state.