Q - How do you make MS Project information available and understandable for non PM team members?
A - Typically this will involve views printed to PDF, exports to Excel, sometimes people have experienced Project Server and the answer will involve web based reports.
Q - How does MS Project determine a task is on the critical path?
A - If total slack is <= 0 it's on the critical path. Depending on the version this can be configured.
Q - What is critical path?
A - It's the longest path of tasks to either a deadline or the last task in the project.
Q - Do you set predecessors or successors to summary tasks?
A - Depends on who you ask and your organization may have guidance on this. Personally I never do this because it tends to hide tasks that may be on the critical path.
Q - Do you prefer auto schedule or manual & why?
A - Again, more of a discussion point. There are reasons that both make sense. I use auto and sometimes set constraints on a tasks by task basis. Small schedules sometimes are better off with manual scheduling. The more experienced someone is with MS Project the more likely, I believe, they are to use automatic scheduling.
Q - Say someone wants a custom view for their team, how might you do that?
A - Usually the answer is to set up a custom text field with a pick list, assign the team names to the tasks, filter on that field and either print to PDF or export to Excel. A more advanced solution is to create a custom view.
Q - Tell me two ways to filter in Project.
A - One is with the Auto Filters. Two is to create a custom filter.
Q - Have you used resource leveling? What are the pitfalls?
A - Again more of a discussion point. The biggest pitfall can be that leveling can push tasks around time wise if it's not set correctly. Most folks don't like that.
Hopefully these questions stimulate a conversation & some reflection on the tool. As you know MS Project is very rich and thus very complex. There is almost always more than one way to do anything.
Hope that helps!
Edit: One more -
Q - When would you NOT use MS Project to schedule a project?
A - "Small" projects. To me that means not more than 50 tasks and not more than a month or two in duration. An exception here is if it's a program that is made up of many small projects that all need to be linked to show critical path or reporting across the program (or portfolio)