A lot of employer's I've interviewed with always make the mistake of asking me about my design decisions. I can't explain why I like one green over another. Sense of style and identity are things employers should just analyze from a portfolio. The real questions that should be asked have less to do with design and more about work habits.
Q1. How did you get into design?
I'm only 21, even in my young generation there is still not a lot, if any, academic support for web/mobile/graphic designing or programming. One great thing about most older designers today is that they didn't have the opportunity to just take a class, or even be offerred a major in college to learn their skill. They are self taught and you, as the employer, can rest easily because they are go-getters. If a new trend or technology comes out, you can bet your lucky ducks that these designers will learn it on their own.
If they did take a couple of Photoshop classes, ask them what made them take it? It's important to know the history of your designer because there are so many entries into this field. Unlike being a doctor or a lawyer, designers didn't all go to college and grad school, take a test, and work at internships with the same five companies.
Q2. This really isn't a question, but I would ask to see their portfolio, and purposely make a negative comment about their design.
See how well they handle criticism. 90% of the conversation between my managers and I is them giving me criticism, and the other 10% is praise once I've worked those suggestions into new changes. Attitude is a huge criteria for a designer.
Q3. What is your least favorite thing to do as a designer?
You want to ask this question to see if the designer, as a worker, is a good fit for the company. For instance, if they are terrible with checking their email, and your company lives off email, then they won't be a good fit.
My pet peeve? Copy-writers who tell me "Why don't you attempt the copy first and we'll fix it from there." This is when I start getting goose bumps because I'm a terrible writer and as a designer it's the last thing I want to do. But time and time again people have always insisted that I attempt it.
Q4. Walk me through your initial design process.
It's important to ask this question to see if the designer includes other people in the planning process. Are they arrogant and want to design just for themselves? Or do they use the wisdom of crowds and partake in researching, sketching, and talking to clients? A lot of artist and designers like to do personal side projects where they only have to satisfy themselves, they may have forgotten how it is to work with others.