Interview questions for hiring GIS Analyst?

How do you handle boring repetitive tasks?

If the answer doesn't mention scripting or automating then you should be wary. Candidates should have come across a scripting language or macros at some point in a GIS course.

What database experience do you have?

Many GIS analysts become responsible for geodatabases - whether or not they wish to or are suitable. Any experience with creating databases, primary keys, SQL, foreign keys etc. is going to be a big plus point.

What are the differences between raster and vector data?

I'd consider this the fizzbuzz test of GIS.

Ask them about their love and passion of GIS analysis. What have they done out of intuition following a lead on a project? What kind of analysis have they done out of pure curiosity? and ask for specific examples

Duties of a GIS Analyst can vary widely. For the last slot we filled, ArcGIS Server administration was a requirement, and all interviewed candidates had experience with it. We got them up on a whiteboard and had them, in as much as confidentiality would allow, draw detailed diagrams of ArcGIS Server setups they had configured/worked with in the past. This allowed us to get a good understanding of how much they understood the guts of one the systems/processes that we really needed them to manage.

Use your whiteboards, make them draw and diagram things out.