My worst concern now would be network security. With root access, it is trivial to e.g. install spambots in all your containers (just checked, command execution works, and external network access is enabled). I think it is a good idea to at least disable networking. (Update: and use a minimal Docker image like Alpine Linux).
Proof:
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Disclaimer: Absolutely not a security expert, just someone who is somewhat on the hook for security!
https://github.com/wsargent/docker-cheat-sheet#security-tips
Probably the biggest one is to use Virtualbox or another virtual machine so that Docker isn't your only line of defence.
Maybe Jessica McKellar's "Building and Breaking a Python Sandbox" talk can bring some ideas. (But maybe not! It might be too Python-specific or too language-level whereas you want to remain at a higher level with just Docker)
Video: https://www.youtube.com/watch?v=sL_syMmRkoU
Slides: https://speakerdeck.com/pycon2014/building-and-breaking-a-py...
SELinux also helps, from what I've read.
Looks like you've got a Hacker News effect on your shoulders. :) Servers seem to be overloaded.
https://scastie.scala-lang.org/MasseGuillaume/62vmEr9XR0qDWw...