edx-platform before 2015-07-20 allows code execution by privileged users because the course import endpoint mishandles .tar.gz files.
Studio in Open edX Ironwood 2.5, when CodeJail is not used, allows a user to go to the "Create New course>New section>New subsection>New unit>Add new component>Problem button>Advanced tab>Custom Python evaluated code" screen, edit the problem, and execute Python code. This leads to arbitrary code execution.