A few that I particularly like:

1) Explain a p-value
2) Explain how diversity reduces error and bias in ensemble methods
3) How do gradient boosting and bagging differ theoretically (and in deployment within a system)
4) Name and explain 3 different dimensionality reduction strategies
5) Explain boostrapping and its practical uses in machine learning
6) Explain the math behind PageRank and how linear algebra in general can be used on graph/network problems
7) How would you explain random forest to a kindergartener using the objects in this room
8) Explain one contribution of topology/geometry to the field of statistics and machine learning in detail
9) When is it not appropriate to use deep learning methods on a problem
10) Explain Bayes Theorem in layman's terms
11) Why is a control group necessary for testing

Those should cover a breadth of important topics and give an idea of a person's depth as a data scientist beyond knowing the basics behind buzz-words.